At the moment they have the option to renew their existing plan OR select a new plan

This is the only available method. They'll need to essentially "upgrade" to one of the other durations.

Yes, but you'll need to edit your plans and add a condition to them on the Workflows tab to only be available if the other plans are not actively subscribed. That's a show/hide scenario though. The best I can suggest is enable pro-rating so it'll apply the remaining value of their previous subscription to the new subscription. It doesn't extend the duration, but it's sort of a refund almost as the value they didn't use is applied to the new subscription.

Thanks Krileon. Would it be an option to use a SQL action to change the NEW subscription start time to be equal to the end time of the current subscription?

I suppose that's a possibility, but I don't recommend it. You'd need to adjust the _cbsubs_subscriptions database table, but if your query isn't 100% correct it could screw up your users subscription or other users subscriptions. So please test thoroughly. This still doesn't really help the fact that the previous plan isn't technically "active" anymore so their new subscription won't immediately do anything. I still recommend using prorating or conditions to prevent upgrade until expired.

The problem with pro-rating is that we lose money unnecessarily every time someone renews. Not what we hope for - and not what the customer intends either.

Prorating doesn't apply to renewals. It only applies to upgrades. For example if I'm subscribed to Plan 1 and I've been subscribed for 3 out of 4 months yet I paid for 4 months. Lets say I upgrade to Plan 2; It'll then take my remaining value (1 month) and calculate its dollar value based off the price of the plan and subtract that from the cost of Plan 2. It causes the customer to simply not lose 1 month of payments unnecessarily. This is only done on upgrades. Renewing Plan 1 while subscribed to Plan 1 does no prorating and you pay the full amount to renew.