Speed didn't increase with downshift

Depends on what you are towing or driving. All vehicle have limits and when towing or driving close to yours there may just not be enough power to accelerate quickly. I assume that it will eventually gain speed if you continue holding the throttle open.

It is not enough to just downshift, you have to step on the gas. It is also possible to cruise on level ground as speedsthat you don't have enough power to maintain on a grade. You don't get full power until the throttle is floored at 4000-5000 RPM.

I've been able to accelerate on 5-6% grades, after being slowed by big trucks, but this would be in the 35-45 MPH range, and in 2nd gear, same gear as 3rd on the 5-speed.

It just depends on grade and speed. If grade and speed needs 400 hp for your weight, and you can get at most 250-300, under very specific speed and gear conditions, you are going to slow down to a speed that matches the power output. Your RV is not going to perform like a 200 hp, 4000 pound car on grades. To do that it would need close to 700 hp over a wide range of road speeds, and simply doesn't have it.

We have V10 but the earlier transmission called 4R100. You should have 5R110 which is also called TorqShift. I can say the V10 package is a very "busy" sounding setup. Ours seems to downshift when I wouldn't think it should need to, and a lot of revving noise comes with it. Our chassis doesn't have a tach so I can't put a number of RPMs difference on it.
I've driven the TorqShift a few times and it seemed to manage shifting a lot better. That button on the end of the shift lever causes TorqShift to do a lot of tricks not possible with 4R100. Are you driving with that switch in the Tow/Haul position or the "normal" position?

Down shifting into 3 will give you more power for pulling not speed. Higher gear and more torque will give you speed. Also don't forget that a MH has the aero dynamics of a small barn so the faster you go the more air you are pushing, slowing you down.