Let's see if I get this right: you've chosen to use your own computer, at your expense, for the benefit of a company for whom you work, when the provide you with computer(s) to use without said investment. But, when they say you have to secure your machine to comply with regulations (probably HIPAA) by installing whole-disk encryption on it, you complain. Get over it. Either install the same software at your own expense (probably the PGP WDE) or let them install it. Since you back up your computer you should have no issue. The problem of slow compute after WDE is installed was true with older releases but no issues that I know of recently.
Here is the problem: HIPAA requires certain things and your employer's legal staff has set standards for compliance that they are satisfied will fit into the regulations. In their mind, until you have all the t's crossed and i's dotted, you are creating a legal problem for them. Legal problems typically become employment problems, particularly for the employee.
In the Federal government space, they won't let anyone, even contractors who have NO government provided computer, to plug into a Fed Government network (physical wire and Feds do not allow wi-fi). Every contractor runs around with a broadband card sticking out of their laptops. Even then, contractors, from clearances for SBU data and up (that would be practically all Federal data BTW), have to have WDE. Healthcare has similar requirements and it's just a battle to lose to try and fight it. You are not even on moral ground here, you just need to suck up and either fix the encryption problem or stop trying to use your personal equipment for work.