I have the same cook top in my Safari.
I would remove my M/H from the shop, and contact Seaward for help. There is no reason your cook top can not be fixed by someone who is competent in cook top repair.
MOST RV techs know nothing about stoves with thermocouples. This is a marine cook top used mainly in boats. The tech wants to cover this a-- and install all new parts at your expense.
MY cook top did the same thing. Light and then go out. OR the knob had to be held down for several minutes and then it might not stay on. THE FOLLOWING IS NOT RECOMENDED, BUT IT FIXED MINE. Since this is a marine cook top and propane being heavier than air, if the flame went out, and the propane settled in the bilge, a explosion could occur.
Now in a RV, we have no bilge, thus MOST RV cook tops do not have thermocouples, thus most RV techs have no clue.
On my cook top, I took the gas valve apart, the slider, that is held open by the magnet that is powered by the thermocouple was slow to react to the thermocouple. I went to my local hardware store, bought a couple of springs that would fit inside the gas valves and hold the slider open. Once you get it apart, you will figure it out.
Now my cook top is like the other 90+% of RV cook-tops. Except it has a electric ingniter. Turn it on and in less than one second, it is lit. Turn it off and it is off.
If it blows out the gas will stay on. No big deal for us. We are always in the RV when we are using the cook top. Cost to fix, less than $1.00 for two small springs.
'96 Safari 3540, 300 CAT, Fulltimmer since 2000