For me, too, this is a revisiting of something I read in childhood, probably around age 12, in the 50's.
I remember Leinster as having an extremely overheated style-- The King raged! Fighting-beams lashed out! Mighty energies raved uselessly through space!!-- and on reviewing it, it's not as bad as I remembered.
Now, this is 1940's/50's pulp scifi, with that kind of sensibility for the most part; things are kind of simplistic, I'll leave it at that. (begin spoilers)
btw, I'm looking for another Leinster story, and I don't know the title. It's about a parallel universe ruled by descendants of Egyptian pharoahs and hyperintelligent wolves called rukhs. You can get from Central Park to the alternate universe by going through some magic bronze mirrors. If anyone can tell me the name or where to find it, I"d be grateful.
Back to the Last SpaceshIp: pretty good read, probably even if you're new to it; very pleasant for someone who read it way back when. Definitely worth the $2.51 I paid for the Google E-book. I guess it might be worth $8.73 plus shipping on Amazon Marketplace; I don't think I'd pay any more than that. And, btw, there are some typos in the e-book edition I read. But it's very readable.
Like a lot of that genre, it moves along smoothly, and has a lot of interesting ideas. There are four technologies that set the stage: the Disciplinary Circuit that allows governments to control their citizens by inflicting neurological pain, the death rays (ponderously called "fighting-beams") that had put an end to war; matter transmission which allows goods and people to move throughout the galaxy instantaneously, and made spaceships obsolete; and the "overdrive" faster-than-light travel which allowed the entire galaxy to be explored and settled with matter transmitters. I find it kind of cool that the death rays are derived from the disciplinary circuit and the matter transmitters are derived from the overdrive. Many of the plot turns, maybe all of them, hinge on further tweaking of these and other technologies.
So the whole galaxy is wall-to-wall tyrannies enforced by the Circuit, and this one guy gets a spaceship out of a museum, escapes with his girlfriend, and is ultimately able to overturn all the tyrannies, who then, like the Empire, strike back, and there are various modifications of the technologies (for example, the ftl spaceship and the matter transmitter are combined into a transmitter that sends itself anywhere instantaneously and receives itself, enabling intergalactic travel), and ultimately freedom triumphs. I think Jenkins (Leinster) may have been an electrical engineer.
One thing that's really interesting about it, which I didn't really pick up on as a child, was the treatment of women.
To begin with, the tyrants use the Disciplinary Circuit (hereafter DC) to make harem slaves out of women; later on, they invent a version of the death rays that only kills the men on a planet, so they can then move in and have all the women.
The hero, too, uses death rays and DC that affect only the men, so that the women can move in and get the job done.
So, despite a very sanitized, sex-free 50's sensibility, and a few stereotypes about women-- "I can't talk to her with you there, because I'm prettier than she is"; "I better not go in that mansion because I'm a woman and I'd want one like it"--
what it has is an awareness of the human race having two sexes of equal importance, and the ability of women to do all the things men do if they get a chance. My favorite line in the book is this: at one point, the hero and his wife are going to take great risks to try to save the world(s), and she thanks him for not worrying about her, for allowing her to take the risk with him-- and he says, "You're too useful" (to leave behind)!
Pretty unusual stuff for that time period. It might make a pretty good movie, or maybe a miniseries, in today's market.
Of course there's no character development, the dialog is just utilitarian; Shakespeare it ain't, or even True Blood. But it reads OK, can pass a pleasant hour or so.