I would implement an AXI4-Lite slave interface with a "virtual" register such that the write to it would push that data item into a FIFO. The rest of your system would stay the same - unless you also want to control start/stop of your IP with a Microblaze as well - in that case you will need to implement another register which would start/stop your IP.
One problem is that Microblaze is going to work with 32 bit values, while your data items are 40 bits long, in this case you will need to either implement a pair of "virtual" data registers and rely on MCU following certain protocol (say write MSW first, then write LSW, which would trigger adding the whole thing into a FIFO), or do both writes into the same "virtual" register.
When I talk about "virtual" register, I mean that CPU performs access to a specific address, this access isn't actually stored in a physical register, but instead causes some kind of side effect (like writing into a FIFO).