OK, you're just describing my 11801. BTW I just bought an SD-32 for $500 :-) Speed limit? What speed limit?
Interestingly, random sampling has a major advantage though I've not seen it exploited properly. My LeCroy claims to have it, but I've not observed its implemented in a useful fashion. However, I don't have a way to get machine readable data out of the DDA-125 yet.
Aliasing arises because the Fourier transform of a periodic spike series is a periodic spike series. The Fourier transform of a random spike series is a single spike, so aliasing does not take place. I first encountered the concept in a dissertation by one of Mauricio Sacchi's students at Alberta, but was completely unable to understand what was going on. The focus of the work was regularization of irregularly acquired data via the minimum weighted norm. It enjoyed a brief period of interest in the seismic processing community, but then faded away because of some mathematical issues which had made me drop work on an implementation.
However, David Donoho and Emmanuel Candes showed that random sampling was a major advantage. Donoho developed the idea and coined the name "compressive sensing" but it was part of a staggering burst of work he did in conjunction with Candes. There is a catch though, sparse L1 pursuits, the term I use because the application of the mathematics is so much broader than just data acquisition, is computationally intensive. When they first started doing it for MRIs at the Stanford pediatric hospital it took many hours to process the data. I know that significant speed ups were developed to replace the original linear programming solution, but I don't know what the state of the art is now. I've not read any of the professional literature on the subject since 2016 which is almost an eternity in a field evolving as fast as sparse L1 pursuits.
Leo's pulser with a 1 MHz clock will do a very good job as a pulse source for TDR using a DSO. Once I get mine and the resistive splitters I ordered from China I plan to do a long thread on using TDR to solve vector network analysis problems. the major problem with the typical DSO is the rectangular passband results in severe ringing after the step. So you need about 3 m of cable for a delay line. But once you can window off the reflection of interest, it's trivial to get magnitude and phase over the BW of the DSO with 100 dB dynamic range. So adding VNA capability to a $400 DSO with an extra $100 in accessories should be a real boon to people interested in HF radio construction.
I'm also going to consider trying to beat Leo's rise time, but I'm not really likely to succeed. I'm hoping to find a dead SD-24 cheap enough I can disassemble it and study the Tek pulse generator.