I really liked the FlexLogix when it came out, but they never quite caught on like the CompactLogix did.
You are correct that the 1794-AENT is the most straightforward way to connect the existing FLEX I/O to a new controller, using ordinary Ethernet cabling and an ordinary Ethernet switch.
I checked the capacity of those old FlexLogix and the -L34 had just 512K of user memory. You can check the memory usage in RSLogix 5000, but only the very smallest modern CompactLogix (the 1769-L16ER) has less memory.
You could use a 1769-L32E or -L35E and probably run the same firmware. Or you could use almost any modern member of the CompactLogix family, including the current generation's smallest controller, the 5069-L306ER.
The internal tags created for the FLEX I/O modules connected via a 1794-AENT should be very similar to the ones created for the local FLEXBus connection, so the conversion should be straightforward.