Can I reduce hot water distribution delay with thinner tubes?
You could try to split the difference slightly "bathroom weighted" and branch off to the kitchen down the line so that the cold water column is reduced to either fixture once one has operated it's a little difficult to calculate gpm based on pressure and pipe diameter. Also static pressure will drop with a draw. You can't calculate that without a field test. 

In order to calculate gpm based on pressure and pipe diameter you need to solve the bernoulli equation. It's not a simple task and there are many aspects that are easy to mess up. I don't know it well enough to discrbe it and I have never used it in practice. If you did want to try 3/8" pipe (uncommon for domestic supply) pick up a roll, attach one end to a hose bib and measure gpm with a large measuring cup. If 10 seconds gives you half a gallon (it probably won't using this figure for clarity) then 1 minute would give you 3 gallons thus 3 gpm. 

Keep in mind a typical kitchen fixture is about 2 gpm. If your setup allows for a comfortable 100% hot at the outlet you will want to measure close to 2 gpm from your coil and use that as your max length. 

Also when using solar and staying off grid etc. You need to consider legionnaires bacteria. Passive control of the domestic hot system can lead to a problem with the bacteria. Stored water should be above 140°F 

Here's an example of how to pipe in the hot water