Some strategy and tactics tips for a 3 rune win with GrFi:
Starter advice and lessons from my own pitfalls when I started crawling:
Weapons and fighting: Always break down packs of monsters. Move packs to corridors and fight one on one whenever possible. Move out of line of sight of things that can smite you, double back through another corridor and hit the pack in the back where the smiter is. If you feel strong enough, carve your way through easy mobs and deal with the smiter first. You can skip monsters. Plenty of Exp to go on the next floors, promise.
Consumables: Identify and USE them. Do not hoard, I've done this and it will kill you. Especially scrolls of teleportation - those are usually abundant and you are most probably prone to finding the wand. Use pots. Crawl is about not dying - you must NOT die at any cost. If you learn not to die, you will eventually win.
Evocables: Use them. Identify them. Possible uses you may have not though of: Polymorph Ogres, Hill giants and the like - they may turn into something completely incapable of using that giant club. Definitely blast hydras with all you've got if you can't run away. Do not poly, dragons may appear. Get those phials and lamps of fire, try out the rods. I personally train Evo to ~10 for midgame (identifying wand charges, enhancing wands and others).
Invocations: I am addicted to Makhleb, so this will be very specific and opinionated, ignore if you think it's bad or if you take other gods: I get ~10 invo the second I step in Lair 2 or 3. I then use major destruction to harm packs of D. Yaks and Elephants to great effect (I then pull them to places I can take them 1:1 though
). If you can squeeze about 15 invo you're pretty set for greater demons. If one appears hostile, get another one to deal with it.
Spellcasting: I have had characters with none that were still successful. I guess it depends on the heaviness of the armour you are wearing. You can completely ignore this and still win.
For your case: Try Makhleb, you seem to enjoy healing on kills, he has easy piety and still has summons. And he has no good-guy conduct. Anything is fair, anything is allowed.
As for weapon choices - for maces - early whips are useful if they come with the elec brand. Other brands for a whip do not really have high impact on the damage you are causing. IF you get an elec whip, get 12 M&F and ignore the skill through Lair. If you don't get one of those, take the most damage heavy weapon you find, preferably branded and train for that.
I usually like to have a shield on my GrFi and my M&F choices usually go Early: Whip (Elec) or Morningstar, Mid: Stay with Elec whip or that Morningstar. Cross fingers for demon whip (those are very findable) - enchant and brand as needed. Late: Stay with DWhip and pray for Eveningstar for high AC enemies.
In truth, you can win with a Demon Whip. I like Eveningstars for the burst.
If you go twohanders, someone else will have to provide advice.
As for Invisible Horrors, try luring them in a corridor and then moving back and forth in it to hit them. Alternatively, if you know what side of you they are on, just stay in one place and swing to the side (with CTRL+direction). Since you are a Gr and I assume you have high AC, there is a low chance you'll lose the fight this way. If it's too early though, just bail and forget about it.