Some sound editing programs (I believe Audacity is one) will let you play your 78 at 45 or 33 rpm, and electronically speed it up to the proper speed.
And some turntables on sale now will play at all three record speeds, including 78 rpm.
The tricky part of these solutions is finding a needle that fits the 78 rpm groove. The stylus was about three times as wide at the microgroove LP needle.
I’m unfamiliar with Vaughn Meader but this thread put me in mind of David Frye’s Richard Nixon: A Fantasy, an LP I listened to over and over and over, and which I can still recall at length. Some of the best parts were throways (e.g. a Ronco-style commercial for an album of famous concession speeches).