There is no way for a Warlock to get access to above 1st level spells from another classes' spell list without multiclassing
Outside of the existing Eldritch Invocations (i.e. Whispers of the Grave allows you to cast speak with dead at will), there are otherwise no way to get a spell from another list.
To list some things that won't help you:
Bards can with Magical Secrets, but Bards are not Warlocks, so this isn't going to work for you.
There is the Magic Initiate feat, but it only gives you access to a 1st level spell and cantrips.
Certain races can also cast spells innately (such as Duergar, which can cast enlarge/reduce innately).
However, both of these last two are "once per long rest" (as are many of the Eldritch Invocations, incidentally, such as Sculptor of Flesh, as an example) so does not meet your "consistently" requirement (since I would say "once per long rest" counts as being a "single use solution", as you put it).
So unfortunately I think either multiclassing or simply not having the spell are your only options.