Rather than a new machine, replacing the HDD with an SSD seemed a worthy alternative, and cheaper too!
Very smooth, and the iFixit magnetic mat was certainly better than the paper+tape alternative I used before. The mat holds the screws just enough to ensure they don't fall away, plus you don't have to worry about your fingers sticking to tape (grin). Followed the iFixit guide below:
Follow the instructions and all should go well. Thanks guys for the great guide to give confidence that it can be done DIY rather than paying someone else.