If mine I would assume the freeze plug is metric given the manufacture of the unit. I would use a caliper and measure the hole in the head. (If you do not have a caliper, Harbor Freight sells a digital caliper for 20-25 dollars.) I would also insure the freeze plug was metric and not American Standard they are different. I would measure the freeze plug and make sure it was 4-5 thousands larger than the hole on the head. Heat and cool down contraction will make a too small freeze plug pop out.I was able to find the head gasket ($65) and the head bolts ($130) at a Koti dealer about an hour from my house. I was also found that a bobcat dealer near the Kioti dealer had the core plug in stick for $4.
I am on the fence about reusing the head botls and gasket. They have about 10 minutes of run time on them and I very well could get it all back together and discover the block is cracked. On the other hand, I could snap off an already yielded bolt in the head and curse myself about being cheap when I am grabbing the drill and easy-outs.....
I question if the head actually froze, it seems odd that it went from frozen solid enough that it pushed the core plug out to completely thawed a few hours later. I know when I installed the plug, it made me uneasy how little the resistance was. I suppose the radiator would be the first thing to freeze and crack, I will know once I get it back together. I hope not, I had over 700 in the radiator recore alone! It some strange way, I would rather find out this last problem was my fault!
Some freeze plug specs calls for a .008 thousand size difference between block and head hole size. See if a Unit manufacturing dealer service department can provide the thousandth size difference the hole in the head and the freeze plug.
If that fails buy the freeze plug from a Dealer using the factory provided part number for the rear freeze plug. Also don't assume the front and rear freeze plugs for the head are the same size.