Re: So a dilemma.
The problem isn't poor security practice. It's going about it the wrong way.
Put the authentication into staff ID cards, they're not allowed to wander around without them - yes the same cards that are used to open doors, etc.
If you need to cross-authenticate then add a fingerprint scanner. if someone's got a card and a fake (or dead) finger then you have bigger worries than IT security.
As for slow changeovers - that IS a problem. Fix it. Tablets and Wifi are cheap enough that shared computers should be the exception rather than the norm anyway.