It would be interesting and helpful to hear some system info from the OP what the sampling and range requirements are. It could be that the requirements demand a modern scope with a better sampling system. Or the opposite could be true.
My interpretation of the scope requirements are really basic. I would see it as little more than an ADC in a big box that takes maybe 5000 samples after each Tx pulse and sends this small packet of info to an external processing system. Because the pulse repetition frequency is probably going to be quite low (just a few kHz?) then the overall data transfer should be easy. But this is just my interpretation of a basic concept demonstrator system.
I think the upper limit of the old TDS7404 is 400,000 triggers (or radar Tx pulses?) a second but I'd expect that a typical dev system wouldn't operate a PRF this fast.
So I'm not sure that the slow old UI and other aspects of the (very dated) TDS7404 will matter that much. Obviously, if it was used for other tasks it would be a bit of a dog compared to a modern scope.
I think our 7404 at work is mainly a dust collector these days because the engineers reach for the faster/better/£££ modern stuff instead. I've seen it in use and it was very big and made lots of fan noise so it was not popular in the labs with anyone sitting nearby
Someone mentioned hiring a scope and maybe this would be a wise thing to do even if it just meant hiring a one of the >10 year old scopes like the TDS7404 or LeCroy models for a week.
I'd be tempted to also blag a brand new £££ modern scope on trial/approval/demo and see what things the older scope can't do.