Bi-Amp Mash Up SS on Bass and Tubes on top?

There are amps with variable gain mostly sold on pro audio markets so you can adjust the gain(in some cases sensitivity as well) of the amp in order to match parameters of the trebble amp.

Apart from the extra power each amp handles a lesser frequency range; this usually gives an improvement in sound.

you'll just double the power. more is almost always better.

Hmmmm. so let's say your info is correct. If I do a bi amp with matching amps what would be the advantage or a singe amp?

...only for small volume control ranges with large sacrifice to the dynamic headroom...

The situation is really as follows:

Let's say you'll pick up trebble amp with higher sensitivity.
On low volume levels you'll hear more trebble even from less powerful tube amp and as volume will go up you'll achieve necessary balance that will be fine on a very small volume range. If you listen to the music that changes dynamic large, this set up is not good. In fact any set up that compromises the dynamic headroom downgrades the system and decreases its performance 'class'.

Let's say you pick up the tube amp that has same input sensitivity, but is less powerfull:
In this situation you'll have dominating low frequencies from the very beginning of the volume range...! You can certainly use attenuators for the larger powered amp but still you will face the previously described scenario with loosing dynamic headroom.

The right way to biamp without active crossover is to use 2 identical power/sensitivity amps. Otherwise you'll need acrive crossover between amplifiers and removed built-in crossovers from your speakers.

I am hoping that the effort would result in an even better sound

If it is higher at one watt it will be higher at full output also. The idea is that the top end will take much less power to drive so you assume that it is the top that will need attenuation. I am not sure that in every case it would be necessary for the top to have more sensitivity if that is where you have the volume control as you are likely to be using less power there but it is a good precaution. This combination is a little harder to pull off than tube-tube or SS-SS combinations but many do it, it may just take a little time to sort out.