Well, it would certainly be cheaper, but I can't tell you whether or not it would work. It might, but I don't want to send you down that path thinking all your gearing issues are solved, because they might not be.

You're currently running a 52t chainring from the spec listed above. Whether or not you could fit a smaller chainring to make enough of a difference in gearing is the question, and also, whether this entire setup works smoothly together, because if it doesn't, no sense in going that route.

If you do go the smaller chainring route, you'll probably have to remove a few links in your chain, otherwise you may have too much slack with the smaller chainring and that will cause problems shifting compared to the stock setup which was intended for a certain length chain to work properly with a 52t chainring and 28t large cog.