Omnidirectional speakers will certainly give you an even dispersion of ... reflected sound, but very little of the direct sound that is required for clarity and definition.
Your room has moved from the typical stereo listening space of maybe 2000-2500 ft3 to around 9000 ft3, and that’s in the size range where big room acoustics come to the fore.
In a large space like yours you want controlled dispersion of direct sound, and the only solutions for that are horns or a custom designed line array, engineered to perform like a horn with respect to a controlled coverage pattern. Anything else will, in a room of the described dimensions, 25 X 40 X 9, simply not work well. The laws of acoustics won’t allow it. Understanding why requires a little background reading on RT60
probably about 10 feet. Beyond the critical distance the sound loses definition, becoming muddy and boomy - unless steps are taken to mitigate these issues.
First you need to calculate, the reverberation time for your space, I would guess about 1 sec at 2KHz. Next, you need to calculate the Critical Distance http://www.mcsquared.com/critical.htm http://www.csgnetwork.com/acousticreverbdelaycalc.html, the distance from your source to where the direct sound level equals the reverberant sound level. RT60 drives the critical distance and you can see how room furnishings, flooring, carpet, windows and ceiling impact the result. With ’normal’ room finishes, the Critical Distance will probably be about 10 ft. But, since your speakers will be in the corners at a 45 degree angle, that 10 feet from the speaker front is actually about 10 feet in front of the wall, and center to center about 20 feet apart. Traditional stereo speaker placement, creates an equilateral triangle putting the seats back nearly 20 feet, less than ideally well into the reverberant field. So, how do we reduce the reverberant field level and increase the direct/reverb field ratio? Increased room absorption and controlled speaker dispersion. In YOUR room, wide dispersion is not your friend.
For room treatment, a good start would be 6-4’x4’ 2" Fiberglas panels (or 12 2’X4’) placed to capture first reflections (centered on a point roughly 10’ in from the front and side walls, the others spaced accordingly) and 2-3 2’X4’ panels vertically on each sidewall between 3 and 7 ft out from the corners, centered equidistantly from floor and ceiling. Depending on the rest of the room furnishings, additional absorption may be desirable on the side and rear walls. These panels are readily available online. I have used Acoustimac with great success. They use the proper Owens-Corning rock wool, have a variety of colors and fabrics available and a 2’X4’ panel will run around $70 each.
As for speakers, without getting into vintage or esoterica, you are basically looking at Klipsch Heritage or the upper end of the JBL line. My personal preference runs towards JBL. For your room, The S3900, ~$11K /pr would be the entry level, the 4367 15" Monitor or S4700 Floorstander next up, both at roughly $16.5/pr, and the built-at-another-level-entirely, JBL K2 S9900 at $48,400 per custom built pair.
Big rooms need big speakers. Regular, even great, ’normal’ hifi speakers will just get lost when trying to fill a space 3X what they are designed for.