Well such timescale would in any case depend on EU, not on convenience for any british parliament. There are now N. Macedonia, Albania, Montenegro, [ Bosnia, Serbia, Kosovo ?], Ukraine, Moldova, Georgia, [Turkey ?] all in the queue to join EU. On the other hand, it might help from point of view of geographic and economic balance, otherwise the centre of 'gravity' will shift even further SE away from Brussels. I think to expand EU has to reform processes, to end all vetos and generalise multi-speed / opt-outs.
Meanwhile a new british government could implement obviously convenient win-win cooperation step by step, until there isn't so much left to change. And I'd be happy to see Scotland and Northern Ireland take a lead.