I use Poly Tour Pro as the poly in my hybrids for the last 2 years. I was previously using Apollo pro response (another slick but stiffer poly)
I have experimented with both Poly mains and cross and played with Hybrids for at least 8 years now... so that may give you some comfort from my experience.
If you like the way your current racket plays, then add the non-poly into the crosses. This will mean the whole bed and launch angle will be similar. Spin generation will be less but directional control / ball pocketing will increase. If using a multi in the cross the advise is to go up half a gauge if possible.
If you like the spin you get with Poly, put the non-poly in the main... BUT this will make the racket bed feel a LOT softer, spin will be similar to full poly but balls will fly long if you don't take full cuts at the ball. Also the launch angle is increased.
For Poly mains, these are my top recommendations for non-poly cross:
Signum Pro Ultra Power SF - Syngut. Plenty of power, soft, holds up well (my current choice)
Babolat Addiction - Multi. Has a slick hard coating so life is surprisingly good for a multi. Most club players that hybrid use this at our club for balance of softness/longevity
Pros pro Gutex Utra - Multi. Good control, not too soft for a multi, doesnt have much of a coating. Gives the strings a thud sound, wears out fairly quick but is also very cheap.
Volkl Classic Synthetic Gut - SynGut, Good control, not massive power, soft and slick with the poly to allow snapback
My current DR's have YPTP Poly crosses and I am a 80% doubles player. One is strung Natural Gut in the main and the other with a SynGut - Signum Pro Ultra Power SF. The SynGut in the main does only last about 15 hours but as I string myself and the extra pop it gives me is a good trade off.
BTW hybriding does have a weird side effect in that if you go Poly Mains / Multi cross the strings can last YEARS!!! if you dont hit much spin. like we have people that still have strings from 2 years ago. As the poly goes dead the multis get more powerful so it gives the weird impression that the strings still feel the same. I have a Yonex 89t that has 4 year old hybrid in it, I can take it out of the bag and it still plays great - even though the poly is likely dead.