Yes most modern DVM's are high enough impedance, but for myself it's much easier to watch an analog needle or scope trace moving than numbers flying by. Some DVM's even have a analog graph.
Your call if you want to wait until you have appropriate alignment equipment. My gut feeling is you could get your first IF stage visually better, understanding that you keep track of your starting points and you don't mess with any other coils. Generally it's not advised to adjust anything without having the correct alignment tools, although over the years we've been proven wrong when complete newbies pull off almost miraculous visual alignments. If you be patient I'm sure someone wiser than I will provide alternate suggestions.
Oh, forgot to ask, did you ever get your sound working?