@OP: I don't think single monster models like VG or TG are good choices to deal with cannons... as cannons themselves are great counters to lone models

. High ldr doesn't mean too much unless you were planning on fear bombing.
@wojmir My "nemesis" plays dwarves and hate to tell you, but that is a fairly weak dwarf list. 1 organ gun is very generous but no grudge throwers is a true blessing

. Anvil is a major headache.
Some things though...overall I would focus on downing his units and not stress his siege too much. Once you get into CC, it all rusts anyways.
1) he can't take the same pattern of runes among his siege. That means that only one can be only flaming, the others must be flaming + something else (I think it's called jealous runes).
2) I don't have the book, but I want to say that rune that gives him str 8 (I actually think it's 2 higher than T, making it 7 but...) is a master rune, meaning he can only take it once? Have to ask my friend about that. In any case, if his BSB has it then that means it's pretty squishy since he can't have a shield and BSB (something my friend complains about often).
3)If you want to have a snowball's chance to cast, consider black periapt since it's free +2PD (no use of DD). I don't recommend MotBA since any increase you get will also likely increase his DD, which is not fun. Plus you'll like red fury in CC
4) Let's see, low init units only sporting heavy armor, and ASL? Let's give him a red fury ASF combat lord with str6+... you'll hit on reroll 3, wound on 2 and no saves... may as well be fighting goblins

. Even a thrall with +1str (hit 3+, wound 2+ no armor) would do fairly well. Vamp heroes/lord can (in my xp) eventually carry a combat against warriors. If you're worried about retaliation, consider nightshroud as it will negate GWs. Keep a champ around to accept challenges etc.
5) Lay off the smaller groups against this list. All of his siege excel against small units, so don't give him quite a hayday with it

. If you must use small groups, keep them behind units/terrain that can give cover to deny bolt thrower. Make the cannons do the bulk of the work as they can miss/misfire. Big blocks of infantry force him into attrition fights which you should ultimately win (while his core > yours, your special should > his).
6)I don't know your core, but don't
horde it. This will deny him extra powerful attacks. I personally like skeletons as they are cheap (meaning a LOT can die) and their parry save will come through for you when taking heavy losses.
7) Of course, the real middle finger move is to take master
necro with death and grab purple sun (90%+) and miscast it. A bit unsportsman like, but I'd say so is taking heavy magic resistance against a magic reliant army. My friend once brought anvil of doom (adds DD), banner that adds +2Dispel attempts, and rune of balance. So next time, I showed up with my wife's Bret army and made a list with no casters whatsoever. Since then he's kept anti-magic to a minimum.
8) As I recall, GW GG should trump his hammerers. Nom through those and then head for the backlines or support your dying core against his warriors.
9)Funny enough, ethereals may not be a bad choice here. While I usually don't take them against dwarves, it's because of the grudge throwers aoe smashing an entire unit. In this case, cannons can only take out one at a time, and if you keep them in combat/use units to get cover then bolt throwers shouldn't do too much either. Organ guns can't have runes and so I don't believe their attacks are magical. This is brainstorming, but hexwraiths may work well as they can move through the lines and take out the lone slayers (if they have magic attacks, then opt to move through them to get your damage in). CWraiths are another option as they are easy to give cover and with 3 str 5 attacks, would probably do nicely.
10) Since he splits his bolt throwers so far away, have you thought about having bats dive for one of those? I imagine his slayer isn't close to them and their stubby legs can't move fast enough to defend it...
That's all I can think of off the top of my head.