Cheap smaller front wheel conversion

I want to give more rake to my bike by trying a smaller front wheel on the cheap.

I've been looking out for rims and tyres prices and I've come out with the best solution to choose as a 590 rim (26 x 1 3/8 or 650a)

The brake height is not a problem but I was wondering if I could fit available 23/25 590 width tyres on a rim that is built to accommodate 37 mm ones

I've been reading Sheldon but couldn't find any info on such rims' inner width, although I suspect it should be about 20 mm

And wondered if I could use 700c inner tubes in it by any chance given that it's impossible to find 23/25 590 tubes

Any help appreciated

this is a bad idea

Ah ah! :D

See it as a 30 quid experiment!

Won't the smaller wheel/forks lower your bb and give you a nice low pedal scrape...

I have to agree it's a bad idea.

My intention is to set the bike up for a duathlon and as far as I know they don't allow fixed gears.

A small front wheel would give me close to zero saddle/bb setback and a more aero position, on the other hand.

I would loose the deep v aero effect on the front though.

What should be a minimal bb height for 165 mm crank arms ideally?