Here are a few thoughts...........
Give the worn chain a try, but you know it is already worn which doesn't inspire my confidence.
Make sure you have plenty of chain wrap around the rear cog to help avoid slippage.
I don't trust those half links and have read a few horror stories. If you think about it, the 'S' shape of the half link will naturally try to bend back and straighten out. This seems to be the most common way that they end up stretching and failing.
I have a vertical dropout MTB frame that has been converted to an SS using a rear dropout tensioner. I've had slippage right at high torque moments at the top of hills etc. The drivetrain is new and finding the cause of the slippage took a bit of time. It has drove me crazy for a while because it only appears at that 1% of the time.
* If you have a magic gear that doesn't need a tensioner then count yourself lucky.
* If you do need a tensioner then make sure it pushes upwards and creates some chain wrap on the rear cog so it doesn't slip.
* If you do buy a tensioner, then I think the Yess ETR/B that tensions the front sprocket is the way to go. it has good reviews but isn't cheap.
http://labs.yesspro.com/products/etr-b" onclick="window.open(this.href);return false; It looks much neater in my eyes than a rear dropout tensioner.
* Or shell out for an ENO hub and be done with it. Makes your cheap SS bike kind of pricey at the end though.
* The poor mans ENO is to hack away half of your axle to provide a bit of adjustment.
Surprisingly good results have been reported, but it just doesn't sound like a good idea
Removing gears on a vertical dropout frame can be more of a headache than it seems