You shouldnt have any problems.
I can tell you how I got it working on the TP3244.
My original code is on my other laptop but should give a pretty good idea.
I used three very small lookup tables.
I mask off the first three bits of the dmx value and perform the lookup.
As the first, third, forth, sixth and seventh bits do not change, the lookup table is reduced to only a few values.
I load that to the Hardware SPI, as that is being transmitted I mask of the received DMX byte for the forth and fifth bit.
Perform the lookup, again as only some bits change the lookup is even smaller.
I go back and check for the empty transmit buffer or full receive buffer. Once the flag is good, the second byte is loaded.
I repeat the mask for the final three bit of the dmx Byte and lookup for the third TM1804 byte, check flag and load buffer.
Obviously you would then add your delays for reset etc.
This seemed a very quick way and worked fine.
I will check the code tomorrow to confirm this as accurate, I wrote it a while ago and brain is failing me lately.