I don't think wheel alignment has much influence on the chaintension but think your problem has to be found in uneven worn sprockets or an uneven worn chain. Or maybe the brakedrum has distorted a bit?
I've never owned a bike that didn't have a "tightest point" when trying different positions of the wheel when adjusting the rear chain but if its a worrying amount then some new parts will help as mentioned.
I had a drum once that had gone oval that caused excessive tight/Slack chain but that also showed when applying rear brake.