Because of the heating effect I would not go for a very small form factor anyway. As it is likely about matching and not the absolute value I would really consider a resistor array, like ORN or NOMCT (the NiCr version, not the TaN variant).
For a the ref. arm of the bridge one would not need to have exactly the typical 350 ohms. A slightly different resistor value like 500, 330 or 250 ohm should be OK too. So one could also get away with more normal resistor arrays.
Precise 350 ohm resistor sets are available in the LT5401.