Maximum range of 27 MHz ISM band NLOS radio broadcast
What is the maximum range of a 27 MHz ISM band when transmitting at
  full power?


It depends on power emitted, antenna types at both ends, temperature, frequency, terrain, interference, bandwidth of data and (sometimes) a bit of good luck.

What you should consider doing is following the general rules for estimating link-loss i.e. how many dB is lost between transmitter and receiver in a worst case situation. You can start this process by using the perfect scenario of free-space (i.e. earth to moon transmission) then apply antenna gains and more earthly constraints like fade margin.

Link Loss (dB) = 32.4 + 20\$log_{10}\$(F) + 20\$log_{10}\$(d) 

Where F is MHz and d is distance between the two antennas (kilometres).

So, for an example of 27 MHz and 10 km, the link loss is 32.4 dB + 28.6 dB + 20 dB = 81 dB i.e. not really a problem in free space.

Your antenna types probably won't bring anything more than about 4 dB to the party so link loss becomes maybe 77 dB. Fade margin might be 30 dB worst case for over 99.9% of the time so this takes the link loss to 107 dB.

How much power do you need to receive to form an adequate signal that can be reasonably decoded with an acceptably low bit error rate? A useful formula is: -

Power required in dBm is -154dBm + 10\$log_{10}\$(data rate) dBm

So if your data rate is 1 kbps and you have your receiver designed accordingly to have a limited bandwidth that suits this data rate, your receiver, at ambient temperature requires -154 dBm + 30 dBm = -124 dBm.

Looks like 10 km is doable to me (with 100 mW aka 20 dBm) providing you don't get significant corruptions from anyone else using the band. Unfortunately I cannot help you on this matter other than to suggest you transmit everything two or three times (or more). You could also take steps to add check-sums and maybe error correction codes. Some techniques redistribute the normal sequence of data bits in a packet to avoid pulsed interference killing off what would have been several sequential bits - this allows some error correction methods to work better with interference that is more "man-made".