There are various forms of slot antennas. Because you start with a conductive surface and then cut slots into it, they end up perfectly flush with the surface. Obviously the gap would need reinforcement on the back side with a dielectric material.

RFID tags come in a range of frequency bands. What band is involved here?

Currently torn between HF 13.56mhz and LF 125khz. The reader will be battery powered so energy consumption is very important to me. It also seems that LF performs better in heavy metal environments, which this device will operate in.

Any approximate idea how deep the slots would need to be so that the antenna sits flush with the cylinder face? Or how much of a gap would be required between the cylinder face and the antenna?

Also - how far could I wrap the antenna around the cylinder? Would 180, 270, or even 359 degrees cause issues? The idea here being an antenna that could read a tag from any orientation around the cylinder face.

Neither 13.56 MHz nor 125 kHz "antennas" (of the usual design theories) will fit into the space you've indicated.

If it only needs to span a cm, then perhaps a simple half-transformer multi-turn loop might work. Depending on the reader transmitter, you might need to provide a matching circuit.

I see...Why wouldn't they fit? How much space is needed?

For example, a dipole antenna for 13.56 MHz is about 34 feet in length. There are many techniques to shorten antennas, but for this application it seems best to just abandon the concept of an antenna as such, and just feed a multiturn loop.

Obviously 125 kHz is even moreso.

RFiD antennas are very specialized antennas and normal antenna size dipole requirements don't work. RFiD antennas are closer to wound transformers than they are dipole antennas.
I suggest you attempt to buy RFiD antennas and evaluate how well they work. You need to have a system spec for what will work.
A normal antenna would be a slot with coax across it, and the slot and internal cylinder would be filled with high dielectric and probably lossy potting or MAGRAM, which usually is high dielectric, potting compound and low loss at your frequencies.
Kevin