Your problem sounds similar to what was diagnosed as my second burnt valve in 6 yrs. IMO the engine is worth rebuilding, a well maintained borrom end is usually good for 2-300k, and since it sounds like money is tigh an engine swap is not an option. Unfortunately you really wont know for sure that it is burnt valve until you pull the heads.

To rebuild it it, pull both heads and have them reworked, you don't want to do just one. I had both of mine rebuilt and valves adjusted including new headbolts(mandatory for the 3.0), for about $550 two yrs ago, yours should be cheaper since you have access to a machine shop. You will also need a new knock sensor and knock sensor wire(also mandatory on the 3.0), you will want to have the injectors cleaned and rebuilt, a new timing belt, water pump is fine unless it is leaking(or you can replace for peace of mind), and a complete engine gasket kit. Depending on prices where you live this should run under $1000. To avoid another burnt valve and to increase performance, I installed a set of Downey headers, a new cat and muffler. Along with some misc. stuff my rebuild came in around $2k. No one can say for sure that burnt valves/hg failure is caused by the oem x-over and exhaust manifold design, but with it so common on this engine it seams like a possibility, especiall since #5 &#6 are common burnt valves.

I had never taken on an auto rebuild as involved as the 3.0 before, and it seams a lot more daunting than it really was, you just have to take your time in the pull down stage. I made a drawing, took pics and video of everything as I tore it down. It took about 3 days to tear it down, but the time was worth it since I had plenty of reference material for the rebuild, all those vaccum lines can be a PITA.

Also you can install the heads complete i.e., with the head bolts already in place, the cam installed and the valves already adjusted, there is enough room to get a socket onto the headbolts with the cams in place and still get the proper torque setting, you have to buy a slim socket to do it though. This will save you the hassel of trying to adjust the valves yourself, or towing/driving the rig to a shop to have them do it. I was able to do my rebuild w/o a factor manual by buying a haynes to go along with my chilton's, before startying yours, download the FSM manual from this forum, it would have been nice to have it when I did my rebuild.