If the HAZ is cracking all I can say is keep the heat input and interpass temps as low as possible.
If this don't do it, nothing else I can think of will.
As far as the weld metal is concerned Obewans suggestion is better than anything else I can come up with.
Hey Rick, best to you. Nickel does not do well with either S or Se so use a filler with high amounts of ferrite. You may even consider a 409 filler metal. Keep heat input down.
This is not going to be a high quality weld.
Generally 303 is considered unweldable due to free machining alloys added. Which great increase the risk of hot cracking. Any techniques used to eliminate hot cracking would also be useful in reducing the cracking chances on 303. Such as a convex weld bead. no concave weld craters etc.
perhaps the much more successful route, but the one least tried is to use a low dilution butter pass with a highly crack resistant filler then weld as normal on top of the filler. I.E limit dilution with the base metal as much as possible. I couldn't recommend a filler off the top of my head though. I would pick something over alloyed and something with a high ferrite number which would help in reducing cracking
In order to perform a "butter" pass a low penetration process would be used. GMAW-S has had great success, as well as low amperage GTAW. The butter pass(es) need to be of sufficient thickness to prevent the normal passes from repenetrating into the base material. Once both surfaces of the joint are sufficiently buttered. Welding can take place as normal.
This is an often used technique to weld incompatible base materials by using a compatible filler and limiting dilution.