I used to have the ironing board set up permanently in the SR too. It became more of a place to put things, than to use for regular ironing. I got a piece of the waterproof board that they use behind showers in bathrooms, and cut it to a better size. Then I covered it with 2 layers of wool blanket, and a piece of cotton batting. Then I stapled a double layer of muslin on it. I use it for all my pressing. I can slide it over the edge so I can iron shirts, skirts, etc. Now mine is 24 x 48, so I can open out the 45" fabric and press it without a fold. You could make one to fit the top of your cutting table since you 'never close it up'. You can certainly use the mats and cut on top of that mat (I regularly do), but you can also take it off and lean it against the wall, to use a larger mat.
My sewing table is not nearly as deep as most, only 21". I find it's enough for most things. and it's against a wall. Think countertop depth. You might be able to get a piece of a countertop and put it on 2 file cabinets for support, giving you support as well as storage space. Let's see, Home depot for the countertop, and maybe an office supply surplus store for the file cabinets. I'd replace the dresser with an open bookcase, as tall as you want it - Ikea? They have lots of options and not terribly expensive.
I have 2 pegboards mounted on the walls. One, behind the sewing machines for scissors, etc., and the other on the wall by the cutting table, with my rotary cutters and rulers hanging right where I use them. I also have a corkboard on the wall - it's surprising what you can hang up on the push pins! I also have more bookcases on another wall - not just for books. I put adjustable shelving in the closet - after removing the doors. Bins and those small drawer units fit nicely there. Think of what you can hang on some kind of a board on the wall - and open shelves instead of cabinets.
Oh, I just took another look around the room. One of the doors into the room has a 7" 'lost area' behind it. DH put some shallow shelves there that are perfect for the plastic shoe boxes - now I have storage there all the way to the ceiling (with the step stool that is nearby.) Just be sure to put a label on the side of the boxes so you know what you have in each one. I have buttons, zippers, bias, elastic, belting, velcro, lace, and all kinds of things there.
Good luck and be creative - You don't have to use things especially designed for sewing in your sewing room.