After putting maybe five hours into Avernum: Escape from the pit, doing the quests in the north, retrieving the mayor's necklace and being told to head south west to the castle, I'm starting to find it hard going.

There seems to be nothing worth playing for. No interesting characters, no urgent story line, no exciting and visceral combat effects, no unusual character development mechanics. Most of those aren't likely to change but does the game get a gripping storyline or other improvement later on? Or am I not likely to get much out of it going further if it doesn't appeal at this point?

It's hard to know what you, or anyone not me, would find appealing. The story aspect of Avernum 1 isn't that strong. Various backstories and plots get revealed as the game progresses but if you don't enjoy the gameplay thus far, I doubt things will improve much from your perspective.

I really enjoyed Escape from the Pit and am currently playing Crystal Souls (which has a stronger narrative thus far), but then again turn-based games are almost a requirement for me..

I haven't played Escape From the Pit, only the original Avernum (which is itself a remake of Exile: Escape From the Pit), but assuming the plot hasn't changed completely, there will be no less than three "main" quests to complete, of which you can do as many as you like. But these are not long involved stories with twists and surprises. The game is designed more as a world for you to explore and find your way in, with some epic challenges to tackle as a crowning achievement. To me, the strength of the game was in the writing, if not exactly the story: it was the detailed and well-thought-out setting that kept me interested. There's a lot to find in one's explorations and I was constantly stumbling on interesting places and intriguing mysteries.

So I guess I would say that the strength of Avernum is not in characters, story line, combat or character development, but its world. It's so much more than just a backdrop for your adventures. It contains more than one believable society, with its own ways of surviving the dark caverns, and its own interactions with the other denizens of the caves. Individual characters may not be that memorable, but their roles in the world are important.

If that sounds interesting to you, then I'd encourage you to continue a little farther at least. There's a lot left for you to find. But if the parts of the world you've encountered so far haven't interested you at all, then you may not enjoy the rest of the game either.

There is the occasional bit of descriptive writing that's fairly interesting, but a lot of it is just typical fantasy silliness. I played a bit more and got to just past the tower of magi.

According to the descriptive text the tower of magi one of the most important institutions in Avernum, responsible for food and transport and the main hope of the human nation for improving their lot. So when it's threatened what happens? Does the army get called in? Are there messages sent to the most powerful friendly beings in Avernum? Is it rigged with exposives so it can be evacuated and then blown up?

Nope, the job is given to a band of low level adventurers to solve single handedly despite no previous experience dealing with this type of thing.

I'm giving up at this point, from your answers I don't think I'd get much out of the rest of the game.

In Avernum 3, something interesting happens with the tower after Day 180. Just make sure you are ready for it (in particular, you will want Repel Spirit Level 3).

Note that many players report beating the game before Day 180 on casual playthroughs, or having to deliberately waste time to get this to happen.

You're talking about Haakai Lord they summoned? You do realise it's existance is supposed to be kept secret by order of Linda, one of the Triad that rule over Tower of magi and one responsible for the summoning. Linda is also delusional thinking she can keep it under control (in reality she's under the demon's influence, might've been even before the summoning. I forget.). Iirc only one willing to do something about it is lowly apprentice mage willing to break his wow of silence to get the word out about the situation.

Why would the army get called in? It's a secret. Why would they send messengers out? Why would they rig the tower with explosives? They think they have it under control.

But yes, Avernum is more about exploring an interesting and well written world. There is not much in the way of a plot that involves you specifically, though you can get wrapped up with the Scimitars and Erika.