It is possible, and relatively frequently tackled. You have to scroll down a little to find it but we even mathed the theoretical highest score possible while also doing a three-stamp run. It's 325, but you need to not use a single health scroll until 9 hearts, and corner the gnome BEFORE you reach 10 hearts as well as all the chests. It is very difficult, but with some luck, possible. JUST doing a three stamp run at all, though, is still hard but doable, especially if you can luck into finding Rat King early.
Level XPBank XPGain Extra XP2Lvl
1 0 +5HP -4
2 1 +5HP -5
3 1 +6HP -7
4 0 +6HP +5chest -9
5 2 +7HP -9
6 0 +7HP +5chest -10
7 2 +8HP +5chest -12
8 3 +8HP +9gnome -12
9 8 +9HP -12
10 5 +9HP +9HP -15
11 8 +10HP +27mine -18
12 27 +10HP -21
13 16 +11HP -21
14 6 +11HP +11HP -25
15 3 +12HP +12HP -25
16 2 +12HP +12HP -25
17 1 +13HP +13HP -25
18 2 +13HP +13HP -25
19 3 +14HP +14HP -25
20 6 +14HP -20(-25 to level up)
Total 325
This is an example of a 325 Three Stamp Run giving as much room as possible for the chests/gnome. You see its still REALLY tight.
Math. I went through a full clear run and counted how much exp it took to level up each time, after someone else had gone through and put in a spreadsheet where all the exp in the game was sourced from. After I had that data, I just went through level by level and calculated how to get from point A to point B.
(the autism also helps)