Just strung My ESP racquet with tour bite 16 / discho iontec 16. For normal pattern frame, discho iontec 1.20mm or 1.25mm would be perfect for crosses. It is useless to pay a lot of money for expensive crosses, just because crosses just work for stiffening or softening the overall stringbed. Typically you want a stiffer main, so it will last a lot and snap back for more hours, while you want a softer,slippery crosses, to get the right (right for you,someone wanna a firm stringbed,others wanna a soft one) stringbed.
plus, with a slippery,round, CHEAP string like discho iontec, you lower a lot the stringbed cost. It matters less when you string every 30hours paying someone to get strung, it matters a lot of more if you string for yourself every few hours.
just to say, I love tour bite strings, both the traditional one and the soft one, and I switched to the soft because the regular is too harsh. But the traditional one last and snapback even 15hours, while tour bite soft after 10 hours is exhausted. Plus they cost 6-12€,depending how and where you buy them.
putting a cheap and soft discho/pro's pro/weisscannon etc. string on crosses, you get tour bite tension maintenance and spin, and a softer feeling overall. Plus I think such made poly/poly hybrid can counteract their feeling while going dead. I explain better. Firm poly while going dead becomes stiffer and stiffer. Soft poly becomes mushier and mushier. Putting them together will let you play some hours more, having them balancing firmness and softness.
BUT you have to try and experiment. Some strings have very different response time(dwell time for example) and they could work good on paper but bad on practice. It cannot be predicted easily, just try as general idea to put firm,textured/rough string on mains and soft,slippery,round string on crosses. Adjust tension based on string properties. Softer ones lose more tension even just strung, so give them 1kg-2lbs more, or put the same tension but knowing that you will get softer stringbed.