Advise for new speakers for my basement exercise room

new member. I would  appreciate your expert advise for new speakers for my basement exercise room 15x25. Hard floor and walls with  4 windows and 9' ceiling. I am using near mint JBL 112s but hi frequency sounds are not realistic. Lows are great.  System is Nak CA7 pre, PA7 Nelson Pass 200w amp, and Sony ES707ESD CD player, AQ and Morrow cables.  Like upbeat music for exercise. Don't have time and do not want to go and audition and comfort level is about 5k or less.  My Mission 770s sound better than the JBLs there, but are needed elsewhere.
Thank you everyone for your advise and time.
You said " Mission 770's sound better" I think you have yourself an answer unless you really want something different. Get another set of Mission 770's for the workout room (or rethink what you are doing, use the Mission's you have in the gym, and splurge on a set of something new for 'elsewhere')
Most of the professional work out spaces I have seen use the JBL pro monitors, 4312s or similar.  I would think the L112s should work , but it is all subjective.
I mean, this is not a use-case for high-fidelity critical listening. As others have said, acoustics/room treatment are going to be sub-optimal at best, the listener is going to be moving around the room so listening axis is variable both horizontal and vertical, air conditioning may need to be on..

Good SPLs, dispersion, and ease of use/convenience are needed.

I say just get some bigass active monitors  (e.g Genelec 8350s, ATC SCM25/45As) that you like the sound of and move your nice hi-fi equipment to another room like a home office.
For better acoustics in a room like that, you might want to turn your speakers around backwards.
I would think about how you are going to use the room.  Are you really going to be sitting and listening intensely and critically?  Most likely not - so get some exciting active speakers that are well below whatever budget you have in mind because honestly you want to be focused on the workout not whether or not the sweet spot is just right.  The Klipsch The Fives come to mind but I am sure there are others as well.  You'll want something you can just kick on when you're ready to get moving and then easily disengage from when you are done.  
How bought some ohms? Assuming your going to be moving all around the room. 
Get on the speaker buying merry go round then realize your space is 
really the issue.
In a workout room you have plenty of latitude with 
acoustic treatments mounting and placements.

Just about any speaker will sound like crap in a room like that with all the hard surfaces.

You will have to treat that room. (hint) start with some carpet on the floor, if possible.
Mirage Omni 260.....or

Mirage Omni 60 subs optional.

Sound will envelop your room.....

You will be pleasantly surprised!
I also have a large work out room but I mostly ride a stationary bike. If you are mostly stationary when exercising you can go with very near field speakers and possibly a subwoofer. This set up will eliminate most of the reflection issues. 
My workout room speakers are KLH Model 6’s I bought off Craigslist for $75. They sound wonderful paired with my Fisher 800C tube receiver. However as others have said, you need to treat the room to tame it down and stop all the reflections before you can judge.
My basement speakers are older BIC V-830’s
  absolutely great speakers!

 Bass, mids, and detailed yet non fatuiging treble. 
Try this.....

 cut an old tshirt in 1-2” squares, tape 1 layer over the tweeter, and give a listen, if not to your liking, put a 2nd layer over the tweeter/horn.  And come back with ur thoughts!

 A very easy fix for bright speakers in a basement with no caret, or high absorbing furniture. 
   Before you make a huge move, give a try, 
did this on my BIC dv-84 towers, treble was very over powering with hardwood floors, and minimal furniture to soak up the treble.

  Please try this,  cut small squares, tape over tweeter, and listen, then try a 2nd layer, or maybe. 3rd,....... 
I did it, and it was a fix of a lifetime! Worked wonders!

I am going to advise you to buy revel. The M126 is really great. Also because of the waveguide on the tweeter it controls the sound and reflections very well without room treatment. At the shows people ask where the subwoofer is in the room? Very good sound. They are $4400 per pair. The revel stands are $550. All revels will work including the outdoor models if you want to hang them on the wall. If you live near the Chicagoland area this store will let you demo them in your exercise room so you can hear what I am talking about.
I hope this helps and you can demo them. 
Spatial Audio open baffle speakers, great  speakers that help take the room out of the equation. New M4 $4200. 
I'm with hilde45; treat the room....It must be so 'live' as to make crumpling paper resemble a bass line...😬

Then try a little eq to taste....good luck.
In a gym environment it will be tough to really dial in anything. Just too much reflection. That is unless you do treatments. If you have mirrored walls at all, plus windows you are 2 steps behind the curve. I own a gym, sound quality needs to “get it done” but a high end system is sort of pointless in the type of environment. One thing you might be able to do to help, is ceiling treatment. Another option is simply try moving your speakers around a bit. Personally, I would do the above before spending too much more $$$ on different speakers. Your are hearing your environment, not your gear…
Speaker sound is probably the most subjective ideal in the audiophile realm. If you like Mission 770s and the JBLs, then you seem to enjoy a deeper sound with a bass bias. 
My advise is to listen to a "brighter" speaker (B & W 603 s2 Anniversaries come to mind) and match them with a subwoofer that can be adjusted to fit your preferred sound signature for a 400 square foot room. A REL T/9x would give you the deep bass you crave while having the B & W's with their decoupled (37htz) tweeter and continuum mid-range provide a full spectrum sound. This set up with proper cables and wiring would be about $3,400.00. The B & W's also require solid power so that might require more investment.  I realize that may be beyond the budget of the OP, but a room that size, can easily cost $10,000 to fill it with proper sound. Test listen as many speakers as you can with and without a subwoofer accompaniment to hone in your preferred sound signature. Good luck.
I use Spendors and a big REL sub in a mostly untreated basement. Sounds great and the highs are sweet.
I’m thinking B&W would be the first place to look… with lots of room treatments and carefull setup. The room size is nice… but will need lots of deadening.. 
If you don't consider doing something to treat the room, you're setting off on a wild goose chase, in my opinion.
Probably just need some room treatments. 
Some 242 panels from GIK would do the trick. Knock down those highs and leave the bass along.