Where can I get a better power supply?  How involved is swapping it out?

I think meanwell power supply is the best choice. You can buy it on Ebay or Amazon.

I can successfully print with ABS at 220C, so I think the thermistor is probably properly configured, if it were way off, it wouldn't be able to print at all, right?

I tried setting the hot end to 225C and keeping the heated bed off.  The hot end was able to get to the same temperature (around 220C) as with the heated bed on.  Shouldn't there be more power available to the hot end with the heated bed off if there is a power supply issue?

Is this a modded printer? You are using .92 Repetier, did you set the correct thermistor when you uploaded the firmware?

I'm running a Davinci 1.0 with Repetier 0.92.  In my prints, I have my hot end set to 225C.  When I print, my hot end is consistently around 221-222C, not 225.  I tried running the PID calibration and entering the values from that into the firmware using Repetier Host, but the problem persists.  From what I have read online, others say that the maximum temp for the hot end is 240C.  Why is my hot end struggling and failing to hit my desired temperature?

Your power supply could be weak or bad.  It is widely known that the stock supply is under rated as evident by the pulsating Kids inside the cabinet during printing. You should get a contact type thermometer and confirm what your hot end temp is.  You will probably find it off from reported temp by 10 or even 20 degrees.