I think it would probably work. Since you're adding weight every week, and only testing once a month you will slowly work away from the 70% range, and then come back down once you retest. This kind of waving should allow for long, consistent progress. For instance, if someone's 1RM was 150 they would start at 105 (70%), add 5lbs per week, and end up at 120lbs (80%) on the fourth week.
Alternatively, you could try something like the singles pogram Pavel posted in "<a title="Kettlebells and Deadlifts go Together Like Pickles and Vodka" href="http://www.strongfirst.com/kettlebells-and-deadlifts-go-together-like-vodka-and-pickles/">Kettlebells and Deadlifts go Together Like Pickles and Vodka</a>". So, instead of increasing the volume through the week you increase the weight and decrease the volume. The hypothetical lifter with a 1RM of 150 would go from about 100lbs for 15 singles, to a top weight of 130 for 6 singles, before adding 5lbs the next week.
I just took my single arm press (each arm) from 32kg to 36kg in two weeks by pressing the 24kg every day, but I am covering well-trodden ground for myself and basically just reestablishing some strength I've had previously. I'm going to work with the 28kg for a while and see what happens. I don't have time for the ROP-type pressing volume right now due to my GS work.
I have done it with double presses and it works. rather than add weight every week, I added reps until I was doing doubles every other set. then i went up in weight. went from 2x40 for a max single to 2x48 in about 10 weeks, i think.
Justa style is based off a program bye Steve Justa. The programs start off with a few singles with 70% of your max and throughout the week you add reps. When the week is over you increase the weight and go back to doing a few reps. After a month you re-establish your max and start over with your new 70%. Google can provide you some more info, and Justa also has a book called "Rock, Iron, Steel" which contains a number of routines.
Chris, not quite. I'm doing it every other day and doing GS on the other days. I've upped the working percentages slightly due to the lower frequency. It may not work forever but short-term seems to be working well. I pulled 350 beltless yesterday very easily even though I had not touched anything heavier than 225 for several weeks. I also did the 36kg press and did a pullup with 24kg attached. Nothing super but I'm satisfied given that I have not done much strength work for a long time.
Rob, not to be a 'follow the routine' nazi, but if you're doing it every other day, why not do one of Justa's singles routines specifically designed to be done... every other day? He has at least two of those, I think.
I am currently, and have used in the past, the Steve Justa pressing styles, as well as variations, and have found it to be exceptional for increasing pressing power. Just be sure to increase heavy upper body pulling work, to keep the balance. Heavy rows and pullups transfer to heavy presses.
Rob, Ben and Andy have you covered: 25/12, 30, and 4 are some of the other programs.... The only one not mentioned thus far is this one:
"Singles strategy #5: train two days on one day off, all year round. Work on 10 to 15 lifts every day. Do two singles in each lift with one to two minutes' rest in between. Use 70% of your 1RM. Add 5 to 10 pounds to each lift every three days. Every two weeks, max out and re-calculate percentages."
Also, it's worth noting that 'rock, iron, steel' was apparently heavily edited, Justa's idea of a 'working weight' for the singles programs was basically a moderately heavy weight that could be done with decent bar speed--thus, possibly as high as 80% in some lifts.