Gold
OK here goes. 1st I am going to assume you have a MFWD 1070 and not a 2 wheel drive, although the part numbers may be the same, I just didnt check the 2 wheel drive tire availability. Most of the items you are looking for are available for your tractor. You will have to change rims and tires due to the width of the 1070 turfs the R4s will not fit. According to JD Parts they only offer an R1 tire for this tractor, however given the size of the tire I would call on my local Wingfoot, Les Schwab or other tire dealer for the tires.
Part numbers needed.
Front Rim-- AM877153 -- 38 in stock nation wide -- 5JA-16 size
Front R1 Tire-- M804215 -- 18 in stock -- 8x16 size R1 tire
Front Tube-- M804216 -- 12 in stock -- may not need for tubeless R4 front if you find one.
Rear Rim-- M804692 -- 5 in stock -- size not given in parts
Rear Disk-- AM877620 -- 28 in stock -- you will need the bolts and nuts to put these two items together
Rear R1 Tire-- R54372 -- NLA obsolete part... Tire size is 13.6x28.
If you get the rims thru your local dealer you can call on your local tire company to get the R4's in the sizes stated and you should be ready to climb those 4" banks. By going thru the tire companies you will also save some $$ being that is the bus. they are in. They always beat my prices at the store.
I hope this helps. If your dealer still can not get the rims for some reason they can go through a parts expeditor to get them or at the very least they can get the technical drawings to get to a rim manufacturer and have new rims made for you. I have this done often enough to know it is a possability.
Good luck to you. Enjoy your tractor weather its fun in the mud or working.
JD DLR