We get all the hot water we want in the lav, but only just a short stream of hot water then the water goes cold, even though we know there is hot water left in the heater.
This statement abt your 'lav' hot water doesn't make sense.
For normal operations, you should get approx 6 gallons of hot water before it gets cold..assuming that your tank is 6 gallons.
I'm also assuming that, you filled the (cold) water tank before using it?
You might wanta pull up a chair outside and, listen to your heater..to see if the gas flame is working/cycling properly(time wise)
Are you letting it heat up long enough before using it?
Good luck on getting it working..