I have found a hot-glue gun and thin black foam-core or mat board (the cheap type that is opaque) to be ideal when making darkroom gadgets like test strip printers. A mat cutter makes quick work of cutting the bits to a precise size.
If exposure is correct, that gives you a base. Make one or more contacts changing exposure if you must.
Make your contact print at 8x height and and 8x10 will print at the same time/aperture. With 35 mm. 3.5x 5x 8x 11x and 16x progressively reguire double the time plus resciprocity compensation if you alter time.
Test strip is a narrow strip that spans highlight & shadow. A whole sheet is very expensive and you gain nothing. It does not matter the angle of the strip, just get it to cover the right places.
Lay a strip of cardboard down so you place it properly.
Trust me, sloppy exposures are expensive also. My contact sheets are all uniformly exposed. Saves a ton of time and expense.
I'm with you on this one, Mr. Carnie. I use half sheets (of 11x14 paper), eyeball it for a given density and move on from there. I usually have it close by the third piece. I tried test strips by they don't agree with my brain. I rather make the call from the complete image.
I like your method: f-stop timing easily accomplished. I may adopt it myself, or some variant thereof. Don't know why I hadn't thought of something along that line already (even though working with percentages has always seemed logical to me).
I use a StopClock 500 (RH Designs) and I am happy with its f-stop test strip generation mode. You set the interval, I usually start with 1/4f for new negatives and 1/6-1/12f for ones I know, and just expose progressively shading more of the paper. I would aim for about 7-8 steps. When split-grade printing with this timer, I usually have two extreme grade strips done and evaluated in about 7-8 minutes and I can now move onto the fun part of working out the dodging and burning.
Since i started using a StopClock i stopped making teststrips. I measure out density and contrast with the Stopclock, make a first print and work from there. Depending on the quality of the negative and the amount of effort i want to put into it - the second or third print are already pretty good.