I don’t know. Sounds like it might be worthwhile to replace the timing belt, water pump (because it’s the same labor, basically), and maybe some sensors such as Cam Position Sensor or others, if your vehicle has them.
In this way, if the repair at 125,000 miles was not done, you’re doing it, and the remaining danger to the engine might be a bad head gasket, which is not immediately fatal to the engine.
I don’t know if a mechanic can tell if the head gaskets have been replaced without pulling the heads, which is the same as replacing them. But compression tests could be done. If all cylinders have good compression, there may be a dance in the old dame yet.
These repairs would run a few hundred, and will insure that you can continue with the same vehicle for a time. It’s your choice, but the symptoms you’re describing might be fixable at a relatively modest cost, in comparison to swapping vehicles. Even if you later decide to swap vehicles, the maintenance done should fetch a better trade price.
OK.. Is it throwing a check engine light? If so a code reader will give you some ideas.
Couple of things. As NNB said, compression test will shed a lot of light on the internals. Cheapest scenario is that you have a spark plug wire arcing to the block. Especially if it's worse when cold and especially damp, then gets better when it warms up under the hood. Silicone dielectric grease can fix that - maybe, else new ignition wires. Next cheapest is the timing belt has stretched enough that it is affecting timing. Even if the TB was changed once, at 150k you're due. Seriously doubt that a visual without teardown will indicate whether the head gaskets have been changed if you don't have records from previous owner.
Do the compression test. If it's good, you are probably looking at timing belt/sensors (which a decent diagnostic test should expose). If there is anything flakey w/compression test you can pretty much bet on head gasket (as opposed to rings) due to the statistics of that engine.
Once you know whether or not you are looking at head gasket replacement you can start making decisions. If you have to tear down to do the gaskets, all that renewable stuff should also be changed - why take it all off to put just one new thing on and then all the old stuff back..
Again - look for some of the other signs. If head gasket is starting to fail, popping the cap on your coolant overflow and doing a visual for black crud and a sniff test for exhaust smell in the fluid can give you a heads up on that. There should of course be no black crud in the coolant - if so means oil is getting into there somehow (like through the head gasket ;-)