Labour did try to set a limit on how long you had to be a member for, which caused a fair bit of upset if I remember rightly! It cannot be denied that under Corbyn, Labour membership has swelled. Whether this is because he is pulling members from the Greens, reinvigorating interest in those who had fallen out of love from Politics, or perhaps a sinister plot by Momentum or the Tories to see Corbyn re-elected. It is a difficult thing to decide, and I don't envy the people who have to make that decision. If it were up to me though, I'd perhaps consider some kind of weighted system that takes account of the length of a person's membership, the wishes of the Parliamentary party, etc, but thankfully for both Labour and Myself, I am not on the NEC, or even a member at all.
Regarding the limit, the main reason that caused such an issue was that even after they announced it, their website still stated that if you joined as a member you would get a vote. So people had paid up, and then after the fact, they had one of the "benefits" of being a member pulled from them.
If they are to properly introduce that as a policy of voting eligibility, it needs to decided upfront and properly advertised. As in, they need to say when you sign up you will not get a vote in any potential leadership election until you have been a member for 12 months. That would be the fair way of doing it.
As for why the membership has increased, granted this is just my personal anecdotes and I freely admit I am pretty much right in the middle of the "bubble" in terms of the demographic who has seemed to swing to Corbyn. But from what I can see you are pretty much right. The new members do seem to made up of 3 main groups. Firstly, those who supported a left leaning Labour in the past but drifted away during the New Labour years, secondly those who have been Green / Lib Dem / general lefty politics supporters in the past few years who now see Labour as a proper and legitimate left of centre choice (I fall into this category), and finally those who want to "seize" control of the party aka the SWP lot.
What numbers those different groups come in, tbh I have no idea. My own group of friends tend to match where I am - thought Labour was leaning a bit too far to the right and still unhappy about Blair / Iraq etc so voted for Lib Dems in 2010 (the first time I could vote) but got horrifically let down by them, wasn't that convinced by Milliband in 2015 but still almost did vote Labour but ended up voting Green (I am in Bath, a Tory / Lib dem swing seat, and as I wasn't going to vote for either of those I thought I'd vote with my conscious, and at the time Labour were not opposing austerity). I think that demographic also explains pretty well the number of new Labour members who got denied a vote due to "previously supporting another party".
ps - Sorry for the ramble, only just realised how long this post is now I have finished it!