I'd prefer each .9x equals a new warp factor. Warp 10 is Warp 9.9, Warp 11 is 9.99, etc.
Even at the end of VOY, Fed ships were struggling to hit 9.975 routinely, though Voyager herself was stated to be capable of such. Setting Warp 10 as something that Fed science could do but at the top end, and warp 11 as something aspirational within a decade or so seems to fit better - you don't want to immediately jump from calling it 9.9 to 20 as per your example or you'll confuse the old folk.
Remember, in AGT the E-D went Warp 13 and that was meant to indicate a progression in speed. If Warp 9.9 TNG becomes Warp 20 in your scale, Warp 13 is dawdling. But if it's 9.9999 on the TNG scale... they've gone to plaid.
Actually, during TNG and DS9, most SF ships couldn't really hit Warp 9.75... some like the Nebula class were modified in DS9 to hit 9.5, and the Ent-D was the only one that could hit 9.8 for a small period of time (most of the other time, it could max out 9.6).
The USS VOY was stated on a few occasions its maximum stutainable cruising speed was 9.975 (so, technically, the ship SHOULD have been able to sustain this velocity without trouble), but in actual practice, we never see it happen.
In fact, on several instances in the show, the dialogue actually mentioned that VOY could 'maintain' 9.75 for 12 hours.
Also, in VOY episode 'Threshold', Warp 9.9 was stated to be VOY 'maximum speed' (and that at that speed, the hull would collapse in 45 seconds).
Even in the episode 37's, Tom Paris stated that VOY could technically achieve Warp 9.9 (which in Earhart's terms translates to 4 billion miles per second... or 21 473 times speed of light).
So, 9.975 didn't make much sense when contrasted to TNG and DS9. In fact, the only SF ship to achieve and maintain Warp 9.9 without issues under its own power was the USS Prometheus (as seen in VOY 4th Season).
I'd imagine that VOY could realistically maintain a maximum Warp of 9.75 for about 12 hours (as was stated in the dialogue)... and that its maximum sustainable cruise velocity (one that wouldn't cause the hull to fall apart) would actually be Warp 9.5 (but VOY was mainly seen cruising at Warp 6 - which is excessively slow... at the very least, you'd expect the ship to use Warp 8 or 9.0 most of the time for cruising speed).