Lobelia Sackville-Baggins had an umbrella, and Bilbo had a clock on the mantelpeice. The most advanced thing in Minas Tirith seem to be the siege-engines, whatever they were.
Generally speaking, Tolkien favored art over technology. He doesn't describe Feanor's palantiri as technology; they are art. I think it's not really a question of advancing technology.
In Middle-Earth, I think it's a question of technology-growth being a sign of the decay of the arts. The highest civilizations were the artistic ones (Noldor, and all that high art in Valinor.)
Each race had its art. You might argue that the "art" I refer to is actually a craft, but I would argue that a craft taken to perfection is an art anyway.
For the hobbits, it was actually working the earth. They were superb farmers and gardeners, and they even lived in the earth. When they lost that touch with the soil, and Sharkey built his mills and ugly sheds and started smoking the place out, that was the Shire's greatest catastrophe.
The art of the elves varied, but I think you could examine where the "falls from grace" took place. Feanor & co, is obvioius. Celebrimbor's ringmaking in alliance with a Maia-of-ill-repute comes to mind.
Dwarves are artists in metal and stone.
In terms of men--
The rangers' art is to disappear in the woods and come out again exactly where they mean to. Not much technology there, but lots of "woodcraft".
It strikes me that the art of Bree is that men and hobbits dwell together peaceably sharing real-estate and ale.
When I think of Rohan, I think their horses are their art. Equestrians will understand.
Gondor-- what art have they left? Numenor was once glorious, but their fall was so long ago. They are the most decayed race of all, I think (" How the mighty have fallen. ") They are too busy fighting; not their fault; but Faramir-- a noble example of an "Old Numenorian"-- still loves the arts, and loves the sword not for its brightness but for what it defends. In contrast, Denethor -- an example, I think, of a fallen "Old Numenorean"-- perceives power as the essence of life, and he despairs when it is taken from him. One gets the sense that Faramir could care less about power.
In answer to your question "So how do I write RPG technology"-- my gut instinct is, remember that technology is generally negative and avoid it as best you can. Middle-Earth is about art and character. Whenever technology is mentioned (aside from a hobbits' clock or umbrella) it's a bad thing. Saruman and Sauron are the engineers. The good guys are the artists.
ps. On a tightly related note:
Aiwendil has written an absolutely ***brilliant***, must-read essay regarding the height and decline of music in Middle-Earth.
Aiwendil's essay: Music in Middle-Earth