Halachically speaking, do I have to set my clocks forward one hour in the spring, or can I set them back one hour (this will give me two hours more in my day than everyone setting their clocks forward one hour)?
The latter course of action is not recommended. If you are two hours ahead of everyone else, then that will lead to great confusion, so that those will be "bad hours" - and we specifically pray (in Shabbos morning davening, before Kerias Hatorah) ויציל נפשותינו מן השעות הרעות, that Hashem should save our souls from the bad hours.
So the proper way is indeed to set them forward one hour. In this way, you will be קונה עולמו בשעה אחת (buying the entire world with a single hour).
I have actually seen the Timexer Rebbe put his clock back by 3 hours in the spring in order to always be on time for Tisch.