Coverstitch Machine?

I've always been hesitant in working with knit fabrics, I haven't been satisfied with the finishing I could get on seams and hems.  My attempt at baby merino singlet (without a pattern) although very functional lacked the professional finish I like. It was the first item of clothing used on my newborn - I was worried about the neck size so got that big enough, but the armholes were probably a little small for a singlet! It's getting a bit small for her now and looks more like a muscle T!

Now wanting to do some work with merino and bamboo knits, I started to investigate how I could get the 'double line with back overlock' stitch used on bought clothing.

I initially thought it was just a different type of overlocker I needed and I did one for many $$$$ but then learnt I really only needed a coverstitch machine not a combination overlocker/coverstitch machine that had the added hassle of switching between the two stitch types.

Coverstitch machines are still quite expensive especially when you are trying to reduce expenses with only 1 income and an extra new person in the house :-) I finally decided that a Merrylock 3564 (which I gather is the same as the 3040) would do the trick - now just to sell more items on Trademe (New Zealand's answer to eBay) to raise the money.

All was well till this morning when I realised/remembered that I would probably need a binding attachment to do those necklines and sleeve edges so common on baby clothing.... panic over ... although there doesn't seem to be an attachment for the Merrylock it looks like a generic binder attachment will do... even if I do need to use blu-tack to attach it!