Depends. You can choose to load up your tanks on the boat (if you're just diving 1 or 2... I don't think I'd try it with more), in which case you'd enter the water the same way you do with backmounted tanks. You can also just jump in with no tanks and have the boat crew pass them down. Depending on space/layout, I might backroll in, or just step up on the rail and jump. This is great under certain circumstances. Like someone who is having difficulty with the weight of the gear out of the water - someone with back or knee problems, for example. We're going to Coz in July, and I expect this will be my choice on that trip, because I will be 2-3 weeks out from the end of a 6 week chemo & radiation program, and I expect to be somewhat weaker than is my norm.
A slung tank, like you mention above, is very much the same as sidemounted in this context.
Different experiences...
Can you expand on what you mean by sidemount divers jamming up the process? I've dove off Aldoras boats in singles, doubles, doubles with stage... whatever... never seems to be a problem. Now admittedly, Aldora never has more than 6 in a group, their boats always have plenty of room, and with Sue, Kim and I traveling and diving together, we fairly often (especially if it's not high season) have the boat to ourselves.
Personally, I find things get more disrupted by someone trying to figure out unfamiliar rental gear than by experienced divers who use different configurations.
I don't know how much you've actually dove with people using different configurations, given your expressed aversion to doing so, but you might be surprised. I also have spent a fair bit of time on muscle memory. My single backmount gear is identical to my doubles gear, other than the wing and the single tank. I still dive longhose, my backup reg is still on a necklace, my lights are mounted in the same place/way, etc. Sidemount is admittedly a little different, of necessity, but emergency responses, like donating your longhose, are really quite similar.
Certainly no need for popcorn...