With RS-12, when 10m was open, the satellite could be hard to hear at lower
elevations. However, you could sometimes hear it (and use it) while it was
on the other side of the planet.
RS-12 was my first satellite... I whooped and hollered far more after my first Mode K sat QSO than I did as a Novice and my very first contact. I was able to manage 48 states worked (47 confirmed) and 150 grids confirmed (under my old call AC5DK) to give me an RS-12/13 only VUCC-Sat award. But probably my second biggest thrill was having my CQ answered by OK1DIG while the bird was over North America. I would not call is 'commonplace', but yes, OTH contacts were possible through RS-12/13 in Mode K anytime both 15m & 10m were open between you and the bird. I believe that is what was alluded to when referring to 'stretching the footprint'... HF propagation enhanced, not direct path.
Addressing other comments, no, full duplex was not only not required, but pretty much unheard of on that bird. You found a clear spot on 15m, left your transmit alone and tuned your receive. This meant you had to tune on 'the other guy' and you didn't hear yourself after the QSO began. The primary reason was if you changed your transmit, you could wander on top of an ongoing terrestrial QSO, which was a no-no. And also brings up another big caveat to considering such a bird today, many DX stations on 15m would come through the passband and 'eat up' the transponder power, having no idea that they were, nor should they... it was/is not an exclusive satellite band.
I did acquire a 25 watt 2m transceiver and try mode A for a while, but to be honest Mode K was much easier and I sold the 2m in short order. In my opinion, RS-12/13 was sort of considered like a step child by a lot of satellite purists, in that it was not a 'real' satellite because it utilized HF bands. (Not unlike the 'linear vs FM' or 'HEO vs LEO' debates of more recent times...) And yes, some have pointed out that back then HF was the entry pathway to ham radio, but it was not the radio availability that was the issue as much as the lack of need for directional antennas!!! RS-12/13 was loud enough and heard well enough that I worked it the vast majority of the time with my 100 watt HF rig and a Hustler BTV vertical! (Although I did eventually pick up a used 10m preamp from K5OE that helped a lot with lower elevations... thanks, Jerry!)
And by the way, not only did my rig not do full duplex... it didn't even do split band. I turned a manual band switch knob on EVERY OVER.... for YEARS. (luckily my Heathkit HW-5400 was tough enough to take it) It's also worth mentioning that CW was much more prevalent then and I would dare say the primary mode for that bird... As a matter of fact, the bird even had a 'Robot' that would answer you in CW. You would tune just outside the normal transponder and listen somewhere near the beacon (if memory serves) and give your callsign in CW. If it copied you, it would respond with your callsign and issue you a unique QSO number. (It was not the easiest thing to do, but I know I managed it at least once or twice.) The idea was that you could then submit for a special QSL card. Since I hosted a website and forum for RS-12/13 ops and reported regular news updates on RS-12/13 to AMSAT News Service, I used to get a lot of requests in the mail for those QSLs. (Some even from outside the US!) Unfortunately, the correct QSL address was the infamous 'Box 88 Moscow', and I had to send them all back marked, 'sorry, not the QSL manager'.
Would I enjoy another Mode K satellite? You bet your sweet bippy!!! Would it make for a good entry level bird like RS-12/13 did? Given today's situation (both HF and satellite) and the likely restrictions on a cubesat form, highly doubtful. Do I think it's the best use of resources in today's satellite climate? Probably not. If one wants a beginner satellite these days, it should be something worked with simple antennas and cheap (low power) gear. But looking at an HF only opportunity with limited power budget (and therefore limited bandwidth), I might suggest something along the line of a simple single channel experiment... like the ROBOT, but a voice response instead of CW or a parrot talker maybe. (I can see school kids getting excited that a robot voice talked back to them.) Again, maybe not the best idea, as something digital might be far easier to implement, but just throwing a spit ball here.
Just my opinion and you know what 'they' say about those things... treat accordingly. And while I'm at it, your mileage may vary, batteries not included, no animals were harmed during the forming of this opinion. And thanks for asking the group, Bob... nice walk down memory lane. =^) 73, Kevin N4UFO