When going from a 58, to a 56cm frame, how do I keep all the adjustments my fitter made, when he set me up on the bike? Is it as simple as taking measurements, and duplicating them on to the new frame, or do I need to go back and see the guy again?

This is the first time I've went backwards on frame size, I usually go with the same top tube length, and make it easier on myself.

My main concern would be the stem length. I'm having to run a 90mm on the 58, and it makes it kind of twitchy. How do I figure out which stem to use on the 56? Would I just go with a 110mm, to duplicate the set up I already have?

If you have a printout from your fitter you can use this to replicate measurement.
If not the following should work.
Mark a point on your saddle 12cm from the back of saddle.
Using a plumb line and tape measure, measure saddle setback from centre of BB
Measure from same point on saddle to centre of BB for saddle height
Using a spirit level and tape measue, measure saddle to handlebar drop. With spirit level on saddle measure from bottom of spirtit level to centre of handlebar next to stem
Measure from tip of saddle to centre of handlebar ( I measure to gap in stem faceplate)
I also measure tip of saddle to top of hoods
This should help you replicate your setup if you are using the same bars, brake/shifter levers etc.
Also saddle height will depend on you using the same shoe/ pedal combination on both bikes
Also your LBS Should be able to help you figure out stem length required.

I'm no expert but some basic measurements helped me set up all 3 of my bikes within a few mm of each other.

If any other WW members have anything to add, or have more experience, I'm sure they will help out with advice. I hope I might also learn a bit from other replies

Cheers
Oz

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Ozrider - Western Australia
Parlee Z5 XL 2011 (6055g/13.32lbs) Raleigh RC Ltd 2008 (7.6kg) Reynolds 653 Custom 1990 (9.8kg, now 8.8kg)
The accumulation of marginal gains is what makes the difference between winning and losing

Easiest way I've found is to find a level hard surface with a wall. Place your front tire against the wall and measure to the tip of saddle, center of the bars, and center of BB. Next take measurements from the floor to the center of the bars, top of saddle and BB. With these measurements you can calculate the stack and reach of the center of your bars(X/Y measurements)from the BB, and the height and set back of your saddle from the BB.

When you get your new frame measure both ways to the BB and adjust the others to make up for any differences between BB's between the new and old frames.

The important thing with using this method is that you use the same floor and wall to measure along with the same wheels and tires.

Not necessary to have same tyres & wheels. All that matters is that the wall & floor are vertical & horizontal and the relative positions will be the same.

This will also make your life a little easier www.parktool.com/blog/repair-help/road-postioning-chart. It is an easy to fill out chart to have your current bikes measurements.