Yes. you could do it with the address counters - then wait a moment for it all to settle, then read the data byte.
This solution is sequential only, but for your EPROM exploration - is good enough.
(Note only one 'E' !)
Using address latches etc, is really only needed of you need to access the memory locations randomly (as used during program operation).
The voltages needed for your particular chip need to be determined from the datasheet - it may be 5V only (for read operations), or a mix of 5 & 12V for other operations, or older chips.