Your room is beautiful! I love the roman shades...do they come all the way down? If so, you could just add light blocking material to the back of them. If not, a roller shade behind the roman shade would work too (and might be cheaper)...easy to get up and down...light blocking. They are customizable in many colors so you could find a complementing shade. Here's a link to a place to get some ideas and I have seen these on Wayfair as well (if you can find the right sizes). Good luck...really great room! xx

https://www.247blinds.co.uk/roller-blinds/feature/solar-protection/opacity/room-darkening#isPage=1

Your Roman Blinds are recessed fitted. Therefore, you would not have enough room to fit another roller blind behind them ( underneath the roman blind fittings ), unless you dropped the level of the roller blind. This would probably leave a gap visible from the outside of your house, which may not look very nice.

Alternatively:- You could put up sheer roller blinds and change the roman blinds for a non-recessed fitting, leaving you amble room behind them.

Or, put up voile roller blinds and have curtains.

Or, maybe just window film.

There is a slimline venetian blind, which if I recall has a 15mm vane rather tha the standard 25mm. This might fit behind your roller blind, but i would question whether they would look good in your setting; maybe just using a sheer curtain behind is an option to consider as this would reduce the glare of the sun.