I'm glad that to hear things are stabilizing for you. I encountered a similar situation in that I initially had the probe inside the tub but found the temps fluctuated too much. But when I taped the probe to the heat tape (flexwatt) I really had to crank the temps up to get it warm enough inside. (On an aside, my tub is in the office in my house, i.e. room temp = +/- 72 and I do need a heat lamp to ensure proper thermal gradient.)
What I ended up doing, and it's been successful for me for several weeks now, is I taped the heat tape to a piece of reflectix. I set the tub on the reflectix (with spacers) and cut another piece of reflectix about 4" wide to wrap around the base of the tub. Effectively, this creates a sleeve within which the base of my tub sits. I've found that this holds the heat real well.