Your idea is no-go.
You seem to understand the importance of keeping neutrals separate. Well, the same applies to hots. Anytime hot wires are cross-connected you are inviting all sorts of problems.
Also I don't think you realize the hot wires are on 2 different phases (or possibly 3). Hooking them to each other would cause bang-boom!
If that last paragraph is news to you, watch this video. Understanding multiple phases is really imporatant for "the sizing conversation" we'll have later. I can't have you panicking and thinking you need 200A feeder for 10x 20A circuits.
However, let me do a bit of a "code review" on your setup at large.
The 120V circuits are too long.
My general rule with voltage drop is I don't even crunch the numbers until 170' or so (because default wire sizes are usually adequate). However, that's for 240V circuits. With 120V circuits, voltage drop (by percentage) is double because voltage is half. So 120V circuits need to start thinking about voltage drop at 80' or so.
Also the fact that you have 10 circuits tells me you are adding circuits more often than you'd like.
So you have 10 circuits. Suppose one is maxed at 20A, and the others are quiet - no loads. That one circuit is getting mauled by voltage drop, while the other copper is just sitting there useless. *And I think you kinda know that, and are hoping to "parallel" all that otherwise wasted copper". Nope, paralleling like that is a no-no. causes many problems.
Also you are spending a fortune on wires.
No more #12 wire
I gather you know what a PITA it is to add these circuits, because you have been the one adding them. Well, we're not going to do that anymore. Next wire will be a big fat one that will replace all those #12 runs and solve your voltage drop problem too.
And it'll be laughably cheap. Might even get to use that sub panel of yours!
Run a fat aluminum feeder from the larger of the two sub panels, to a subpagel in your workshop area. #2 will more than support your ten 20A circuits with room for more, depending on usage. (Remember what I said about understanding split-phase? That is important here. Further, if your power is 3-phase, then 1 additional hot wire will give a third phase).
Also we get to significantly oversubscribe circuits that won't be running maxed out all the time, so for instance ten 20A household circuits only need 40-50A of 2-pole/2-phase power, since they are never used maxed out all at once. (if yours are, well, you have to think about that).
- #2 aluminum is 90A per phase.
- #1 aluminum is 100A per phase.
- #1/0 aluminum is 120A per phase.
If you need to pull out of both subpanels, then fine, add another #2 feeder and another sub panel. (they're cheap).
Aluminum feeder is cheap. The going rate for 2-2-2-4 AL feeder (pre-COVID) was about $1.30/foot. Note that if your origin panels are 3-phase, you'll need 5-wire feeder, which may need to be individual wires in conduit.
But you only have to install it once.
Once it's in, you'll be able to support any number of circuits, and have local control of those circuits.
It makes no difference whatsoever, to load, whether you use this feeder+subpanel arrangement, or use individual #12 runs. So you cannot say this will increase burden on what is being done now.
And this will solve the "voltage drop" problem for good, since if one 20A circuit is maxed while the others are idle, the 20A circuit gets the #2 or #1 or 1/0 cable all to itself.