Road fixed / fixed road

I went for SRAM S500 which I believe are reach adjustable

Something that would allow me to adjust the lever reach to accommodate my tiny hands would be ideal.

It would be better to change the bars, the smaller bend radius below the lever of a classic bar inherently reduces the stretch to the lever. Like WhitleyJay, I'm a fan of the OG SRAM shape found on the S500/S900 levers. I don't use the reach adjust, but it's there if you need it.

You can always put a wedge in between the top of the lever and the bar. TRPs come with one as new, but the end of a soft grip clothes peg works quite well at a push. Obviously moving the lever closer to the bar for easier reach means the pull is less so you need to run the block close to the rim. The amount of people that say their brakes were crap after putting the little drop in spacer on shimano levers is unreal.

I'd say the TRP RRL feels closer to a Campag Ergopower lever than an STI. They're my favourite but may not be best suited to smaller hands. Also don't underestimate the effect that saddle-to-bar drop has on lever feel and comfort. The upward-tilted stem and levers suggest you're already trying to compensate for insufficient stack.

Maybe a shorter stem, and brake levers down a fair bit.
I use the TRP rrl levers, I find them very comfortable, and with the reach widget fitted have no problems reaching the lever when "in the drops", I don't have particularly big hands either.

I've had the Sram S500 on two different bikes and I really like them.

I've got a set of these somewhere you're welcome to try, if you like? https://www.sjscycles.co.uk/brake-levers/black-cane-creek-drop-v-brake-levers/

I used to use them on my old SSCX. They're definitely on the small side and were never that comfortable for my massive hands. Plus, matchy-matchy with your stem.