The HR strap with my original 305 didnt have an Ant+ logo on it, but when that fell off and smashed and I bought a replacement, the new strap did have an ANT+ logo, so I would assume that one would work with the 310 and 910.
I'm not sure about my cadence senor. It works with the 305 OK, but I'm not convinced it will work with anything more advanced. I suppose the simple thing to do would be to see if I can pair it up with a mates 910 or the like, but if I was betting I'd say it wouldnt pair.
Of course the cheapest thing to do is carry a small battery charger on the bike and charge the 305 as you biked (I looked at doing it but decided not to bother as to be honest when the battery would run out on the run I'd be knackered, so knowing pace etc would be largely irrelevant at that point in the race. I carried a normal watch with stop watch to let me know total time.