You need to map it all out, and check against local codes.

First problem is getting power from the barn to the house. possibly a
pair of 10KW inverters in the barn produce 20KW, which is 240VAC
at 83A. The barn could be upgraded to a 200A box to make it easier,
did that here. The pair of inverters would feed a pair of 60A breakers
located at the opposite end of this box, from the main house input.
Other circuits in the middle. The 100A feed from the house and the 83A
possible from the inverters will add up to less than the capacity of a 200A box.

Next question is voltage loss in a 700 foot loop of 2/0 gauge copper. Its
resistance is about .0779 ohms per 1000 feet, or about 0.055 ohms for
a 700 ft loop. At 83A the voltage lost will be about 4.5V which will be added
to the house line voltage. Power lost would I squared R, or 375W.

At the house box, the 100A breaker feeding the barn must be located at
the opposite end of the bus bar, from the Power Co input breaker. This
will assure that current from the PoCo and solar are flowing in opposite
directions to any loads, so they will cancel, not add up in the busbar. Some
codes have a belt and suspenders requirement that the sum of all currents
supplying the busbar cannot exceed 240A for your 200A box. In that case
the PoCo feed breaker may be changed to 150A, which when added to
the 83A solar is only 233A.

Having matched arrays and inverters makes it very easy to check for faults.
As long as outputs are a close match, all is well. good luck, Bruce Roe

Company I am thinking of using says they will tap into supply side of barn power so no panel upgrade needed. Is this kosher?

Check your local codes. Make sure the long run is really 2/0 copper, I would consider
the minimum for acceptable losses. It might be aluminum, in that case you would need
to go at least 2 gauges heavier. I use 4/0 aluminum here for 1% loss with 600 ft loop
and 15KW, but you are running 700 ft at 20KW. Bruce Roe

Haven't checked codes but work will be inspected so I assume it's acceptable. Wire IS Alum 2/0. What would loss be with this? I am putting up some extra panels (20.7kW). Extra trenching/wiring would be a big additional cost. Using IQ8Ms and they're also estimating a 1% loss with what's there now.

If the run is a higher voltage AC from the IQ8,s you may be ok. If was a lower DC voltage you may exceed the 2% VD requirement.

Do the arithmetic, aluminum will be around 0.124 ohms/1000 ft, times 700 ft
is .087 ohms, that times 83A is 7.2V or near 3% loss. You can run that way,
esp if your peaks are largely limited by clouds or orientation, but you might
also have trouble with inverters tripping out on high line voltage.

Another method is use staggered array orientation, to spread energy at
lower levels over longer time. This will cost some panel output, I just
bought enough panels to compensate, also handles clouds better.

After 7 years of high AC losses, I buried aluminum triplex direct burial, must
be 24 inches deep. Not that expensive for me since I have a trencher, much
more if you hire someone to install copper. good luck, Bruce Roe