Hey welcome first of all
So efficiency is the wrong mindset with botting, you don't wanna be efficient it will just get you banned quicker (imo) of course there's no evidence for this just what I've observed over the years.
What's the best way to train Construction from level 40 that's both fast and affordable?
Oak larders until you can build mahogany tables, then gnome benches
Are there specific items or furniture that give the most XP per hour?
Using a servant will yield more xp/hr, specific item: basically the best thing you can build that doesn't require multiple items (e.g. bolt of cloth + plank + gold bars etc)
Should I invest in any special tools or boosts to speed things up?
Bell pull, moneybag and a POH with less rooms, and the room that you will build the furniture in must be adjacent to the entrance of the house (aka the shortest distance)
How can I keep the costs down while training Construction?
There is no way to do this unless other bots crash plank prices, but we are doing our part
If anything, you could potentially make 3 side alt accounts, throw them into a decent moneymaker like revs/runecrafter/thieving, mule all the gp over to main and basically get 99 construction off the back of those alt accounts.
Also I appreciate the research into threads, but that one is really old (2020), a lot of things changed since then xD