[MagicRat]

It does sound as if you have excessive valve lash.

My Chiltons manual says the engine has hydraulic self-adjusting lifters, (like most engines have) so no adjustment is necessary.

Then the manual utterly contradicts this statement by showing detailed instructions on how to adjust these valves.

It seems the hydraulic lifters can only compensate for a certain amount of valve train wear.
Beyond that, tiny shims needed to added on top the the lifters to compensate for additional wear.

The measuring tools and procedures for this are straightforward, but not for the amateur. An accurate feeler gauge, spring compressor tool, a micrometer and an assortment of shims specifically intended for this engine are required.

Since Fireflys have not been sold in Canada for quite a few years, and since no other Pontiac uses this engine, a typical Pontiac mechanic (I used to be one) would not be familiar with this operation. I am not surprised they were no help at all.

Try a Suzuki dealership, because this car is a Suzuki Swift in drag, and they would be more familiar with the required procedures, since the engine is similar to other Suzuki products.

Finally, it is possible there are other concerns, like low oil pressure or severely worn or broken valve train components. A mechanic could advice you further on the extent of the repair required.

However, IMO it is more likely that just the adjustment is needed, as described above.