First, congratulations on a very low heating load. Lot's of people would love to have that kind of number!
Let me back up a little and hit some of the questions on this thread and your other post regarrding Delta T
Delta T is a function of how much heat transfer is going on out in your zone(s). Typically in older style systems using baseboard the rule of thumb was a 20* drop. Some systems such a European style panel radiators will function well all the way up to a 30-40* drop while still providing consistent heat. Consistent is the key word here. The nature of a radiant floor dictates that we use a low entering water temperature to begin with to avoid overheating the floor and causing damage to hardwood, linoleum or tile surface.There is also a factor of comfort involved because a surface much over 85* will tend to make your feet hot after a while.
The question then becomes, if we are limited to a relatively low maximum temp,how do we maintain a consistent floor temp from the beginning to the end of each loop. Obviously, if we start out at only 90-100 entering water temp and use a 20* drop the water is going to be rather near room temp by the time it gets to the end of each loop. That will lead to sections of floor with little to no heat output which we would like to avoid as designers of residential systems. That is the reason for using a narrow delta T.
This can be acheived in basically two ways. Flow rate through the zone and the length of the loops. All other things being the same a 200' loop flowing .25 gpm will have twice the temp drop of the same length loop flowing .5 gpm. Loop length also plays into it because obviously, a 250' loop will lose more temp than a 150' loop.
All that being said, it must be noted that there is wide variation in the ability of different types of radiant floor to "process" the heat in the tube. A high mass system like a poured floor can suck heat from the tube like right now. It's not unusual to see well over a 20* drop or even 30+, when you fire up a cement floor at all. On the other hand, a radiant floor driven by tubing suspended below it, will be hard pressed to create a 10* drop . So you have to be aware of the heat transfer capability of the floor you are dealing with too.
As to the tubing size from the Garn Barn to the house; 1" will definitely carry 23,000 btu's worth of heat no problem but I am wondering if you are heating your domestic hot water also and what type of heat exchanger you have on it if you are. That may cause the desired flow rate and therefore the tubing size to increase substantially. My gut level reaction would be to advise you to use 1-1/4" tube if for nothing else than to provide some cushion in your system's capability. You never know what will be needed 5 or 10 years from now. I've never in all my years of contracting heard anyone say "Dang it, I wish I hadn't bought such a big _________ (fill in the blank). A larger bore tube will also require less circulator power to move water from point A to point B.
If all that is a little confusing, let me just recommend that you take your time and keep asking questions until you understand it. There are a more details than meet the eye in any heating system and radiant floors are no exception.