it should try to light but not stay lit.
sense i'm not looking at ur flame on the stove, it is more speculation, on my part, that the gas is ok.
the furnace would be a big user. would think that if it tried to light, it would drop the pressure to the stove.
i don't know if the solenoid has a low pressure override or not but suspect it doesn't.
i would suspect the gas line still hasn't been air freed to the burner. i would do the power shut down then try and put it thru its paces a half dozen times. if that doesn't do it, check the voltage to the solenoid valve.
if i read the manual correctly, u have satisfied all the safeties or the spark wouldn't happen.
as mentioned in other post, there is a high flow shut off inside the propane tank. there have also been those that have had problems with deteriorating pig tails. from what i've read, it sounds like u have checked these out.
without a gauge calibrated in oz located somewhere after the regulator, i don't know of a good way to test gas pressure. when i bought my trailer, they took one of the burner jets off and screwed a gauge on it. it was to sell me a pressure test but i won't go into that.