I think your problem is the hot mash tun. I don't know of any formula that takes into account picking up heat from the mash tun. I'm sure you could adjust current formulas to do this.
I use a standard formula (palmers) and then I have an offset value for temp loss due to my mash tun. When I put strike water into my cooler mash tun I lose about 4 degrees if the mash tun is at room temp. I come very close to hitting mash temps with this.
You could do the same to account for temperature pickup instead of loss. Figure out how much temp your water gains after being poured into mash tun and put that in your formula.
Or, start out cool and come up with an offset to account for that. That seems more reliable to me, but either way would work.
A couple other areas to look at- are all your thermometers right? Also, are you stirring strike water to get a consistent temp to measure?