Whilst building this new line would (I sincerely hope) be easier than reopening the old line through Cheltenham, I think that, should a new line (whether it's a connection to the racecourse from the mainline or an extension of the GWSR) be built, it should be along the old route, including a station that's actually in the town centre. (Although when I say "in", I actually mean "closer than the current one".) However, finding space for such a station would be a little problematic.
I first heard of this proposal in a copy of The Cornishman, the GWSR's magazine, along with a brief response from the GWSR board following its mention at a meeting. The response was, in my opinion, rather negative: whist I wouldn't expect something like "great idea, let's start next week", it was along the lines of "the railway will focus on consolidating current operations", which is fair enough following the extension to Broadway; however, something like "we will consider this as a long term future possibility" would be better.
Anyway, I can't remember the exact figure, but I'm pretty sure that the proposed cost of the link was less than£1 million. How much of the costs would be covered by volunteer time I'm not sure.
I await Network Rail's estimate of several hundred million pounds!