Having made some 5/8 (0.625λ) and 0.64λ antennas I had to stop and think how a 5/8 for 2m could work on 6m. That’s because my antennas used a shunt fed loading coil. A 5/8 is quite capacitive (-jX) and you need to add the same amount of inductance (+jX) to cancel out. Then you have an antenna that is resistive but probably about 200-300ohms, so feeding by tapping the coil about a 1/4 to 1/6th of its turns gets you a 50ohm load. This kind of feed arrangement for 2m will not work on 6m by any means.
There are some 5/8 2m antennas that just have a loading coil and no tapped feed. These tend to look like a reasonable match at 6m but the efficiency on 6m is hugely questionable. Some antennas may work to an acceptable level here, others may be very lossy but still sort-of work.
So there are some 5/8 2m antennas that will be usable on 6m, some will match on 6m but wont work so well and others that will not match.
Back to the OP’s questions about 2m vs 6m. You are going up a wanted summit so make sure chasers know when you expect to be on the air. Having primed the chasers to listen, you have just added a lot of “ERP” to your signal. I would use 2m FM simply because there are many more people QRV on 2m FM than 6m FM. Make a small hand held 3 ele Yagi from PVC plumbing and aluminium rod and you have an antenna that can used vertical or horizontal and pointed to peak signals. A better rubber duck will serve you well for all SOTA activations and is worth buying as well.