What is the Make and Model of this speaker?

You can get a pair of ADS 810s 710s or similar
They sound as good or better than some Speakers in the several thousand range.

I LOVE my Dahlquist 20s. I’d love to get a pristine pair of 10s.

Those quad specs seem odd.  IThe one speced must have a very weak power supply. If so, the quad mode should work better.  My Fisher had 35 wpc x 4 or 90 wpc x 2.  My old Bryston 100 watt amp (3B) is 100 per in stereo and 400 in mono, i.e. two of these would be 100 x 4 or 400 x 2.    

Under 500 the Time Windows would be a good choice. I have a pair I'm not using in excellent condition but I can't ship.

If I were you I would look for a pair of DCM Time Windows. You will find a couple listings on hifishark (ebay).

I can't tell by your profile where you are located. If you happen to be in CA look for a pair of RSL 3600s. They were manufactured and sold there and come up fairly frequently on CL or eBay. You will be astonished by the SQ at that price level for vintage used compared to almost anything.

If you can find them, Goodmans Achromat 400s.

Its a mystery to me should I guess?

35 dB SNR line?  
Good enough for beachside.  
On a calm day.

You have some options with the Akai.  I believe it is a quad receiver or you can run in 2 channels for "double power".  Also, I would be tempted to try it in "quad" mode just to see.  This has all the quad electronics and you might as well have some fun.  I would lean harder toward some higher efficiency speakers and start by looking at that first.  I would be tempted to garage sale some speakers to start, to see how the quad sound is.  From there, they are harder to find these days, I'd go with some JBL monitors or something like the Klipsch Forte.  I drive some JBL 4312's with 35 W/ch and that is plenty loud enough.  Some people swear by Sansui speakers but I have never been able to appreciate.  Good luck. 

Akai AS-980
Specifications

Tuning range: FM, MW

Power output: 50W/ch (stereo), 32W/ch into 8Ω (quadraphonic)

Frequency response: 20Hz to 50kHz

Total harmonic distortion: 0.1%

Input sensitivity: 3mV (mic), 3mV (MM), 170mV (DIN), 170mV (line)

Signal to noise ratio: 35dB (mic), 35dB (MM), 40dB (DIN), 35dB (line)

Output: 170mV (line), 34mV (DIN)

Dimensions: 650 x 168 x 426mm

Weight: 20.5kg