My Ironman is a little too short for me. It currently has what I believe is a 90 mm quil threaded stem. I would like to use a 110 mm steam which would put the reach closer to my other bike. I also am not a fan of the classic drop bars and would prefer a modern compact bar.

I have seen 110mm quil stems but no compact bars that are compatible. I have compacts that I like with 31.8 diameter so then I need a threadlesss stem. I have seen the threaded to threadless adapters. Are those decent options or I am better off going the more expensive route of new headset and new fork (would probably upgrade to carbon fork if I did this)?

get the adapter and fit the bike to you. No big deal, and will look OK.
With the tricolor group, , and black lettering, you can probably get away with black on the stem and adapter.

I used an adapter on my Merckx and I think it looks nice.

A bit of nomenclature rethinking.
You could get an adapter with or w/o a carbon fork that would let you use a modern stem, I don't like the term threadless as all (almost) stems don't thread into the fork.
One way would be a 1" thread less steerer fork. Not easy to locate bur they do exist. You will then need a 1" threadless headset, those exist but are becoming scarce. Then use a 1" clamp both ends stem, aka threadless, but those are not common with 31.8 bar clamp.
Quite a bit to spend, unless you love the bike.

I would get a "quill" to 1.125" adapter and go that route. Keep the steel fork.

Thanks.

On another note, anyone know what size header wrench I need for tange threaded on my ironman? Seems like 32 and 36 mm but I'd like to be sure before buying a wrench

I use the Soma Highway One compact with a technomic stem.
Highway 1 Bar | SOMA Fabrications

I also use the Hwy 1. I find them comfy...but then again I also like the On One Midge. ��

Another vote for the Soma Hwy 1, I have them in silver on my Colnago Master and were just what I needed to shorten the reach, as well as looking better than most compacts...

I use an adaptor on a couple of different bikes and it works well for me and would certainly recommend others try this also. Do you have any specific concerns about using an adaptor?

"One way would be a 1" thread less steerer fork. Not easy to locate bur they do exist. You will then need a 1" threadless headset, those exist but are becoming scarce. Then use a 1" clamp both ends stem, aka threadless, but those are not common with 31.8 bar clamp.
Quite a bit to spend, unless you love the bike."

Not necessarily. Nashbar.com has a well reputed carbon fork with 1" threadless steerer for $99, plus a 1" threadless headset for less than $20. Currently 20% off with free shipping - all costs less than $100. Not too bad. Thinking of doing it myself right now.

You are an Ironman, so keep it cheap and you can maintain smugness in the face of plastic people.
Quill adapter, use a 26.0 stem to keep it petite, both the stem and bars will often be cheaper.
I suggest that 26.0 stems and bars are getting cheaper, and 31.8 looks kind of funny on an Ironman.
You can find the bar you want in 26.0 fairly easily, and a stem as well.

Then go out and pass people.

I agree, and Ironman should not have an FRP fork. Fibre reinforced plastic.

What is the OD of a 1" threadless fork, and a 1" thread fork? Are they the same? Could a threaded fork with a longer steerer tube from a larger frame be converted to threadless by sawing off the threaded portion?

Seems to me that if the OP wanted to keep his bike as original as possible (with steel steerer), the solution would be to locate the fork from a bike similar to his that has a longer steerer tube, and convert it threadless (by sawing off the threaded part of the steerer), and buy a new 1" threadless headset.

You could also try an alloy fork. 1990s Trek composite bikes (or a damaged frame with fork) came with 1" threadless alloy fork. This could provide you with the fork and a threadless headset.