If I just want to do IFR approaches at my class D airport of origin,
how should I file? One FSS person suggested that I file McKinney (TKI)
direct to a 5 mile on a 360 radial from the airport (which has no VOR)
and then back to TKI -- putting "multiple approaches" in the comments
section. Any other thoughts?

Unless they've changed the rules recently, you don't have to file if you
plan on staying with the controller of your origin airport. You just get on
clearance delivery if you have one and tell them you want to do approaches
and they will give you a squawk. You then go from there. I think you could
file if you want to but it would only be to let the controller know what
approach you plan on doing if you lose comms.