H1 is really cool and awesome. It is one of the few adventures that has a huge war and expects the PCs to be in the middle of it. H4 is not. It is like they took anything evil and powerful and put them in a dungeon crawl without really thinking of how it all fits together.
I can't speak much on H1-H3, but I advise you to take H4 and freeze it in carbonite. Then imprison it in the mirror dimension thing from Superman 2 and launch it into space. Possibly at some point nuke it from orbit because its the only way to be sure.
It's far too often over the top goofy, bordering on being a parody of the D&D planes. It's also a playstyle towards high-level play and play on the planes that I truly don't care for. It has a beer drinking, cigar smoking celestial with a texas accent hailing from the fortress of "el amo". The PCs fight a laundry list of demon lords like they're random encounters, etc. It doesn't really seem to take itself seriously and it cheapens the atmosphere of the planes IMO. Basically it's the antithesis of 2e Planescape.
(snip) My advice would be to take the series, boil it down to its core themes, then make it your own. That way, you don't have to deal with Battlesystem if you don't want to, and you can focus on story (if that's what you want to focus on).
I also think an important part of making it your own is getting rid of the seriously stupid names that infest so much of the adventures. Unfortunately, the supporting regional supplement was by a talentless hack known as R A Salvatore. That regional supplement, FR9 The Bloodstone Lands (IIRC), included such gems as a mountain range that was pronounced F YOU. Delightful, eh?
Like Shemeska also advises, kill all the whimsical, silly and real world inspired stuff deader than dead so that your players do not start mocking you and the adventures.