You went the same route I did, haha. Getting an adjustable bridge will let you change the action at will, however, replaning the fingerboard is probably necessary. I can't say it is necessary for sure because I haven't seen your bass, but if it's anything like mine, you'll be much happier in the long run getting it fixed and set up how it should be. Mine buzzed and was uneven, and I assume yours does and is as well. Get everything fixed that needs to be fixed now. Mine turned out to be a great bass. I can't say it enough: Get it fixed correctly.
Also, what type of music will you be playing? Different action and different strings will be required for different styles. You said it came with nylon rockabilly strings (weedwhackers), will you be playing rockabilly and/or bluegrass, or do you want to play another style? Maybe a few different styles? Each style or combination of styles will require a different type of strings and setup. The nut and bridge string grooves will have to be cut according to the type of strings you'll be using, whether that be steel, nylon, or gut.
You should spend the money, otherwise you'll end up with an instrument that is no fun (and painful!) to play. You really need to invest money in lower end double bass to get something decent. What kind of prices are you talking about? $300-$500 is the range you should expect to pay for repairing a bass of this level in full, or at least it is around there in my experience. The trick with ebasses is that they come in poor condition, and not only need to be set up, but repaired as well. I paid somewhere in this range to get mine fixed.
Have your luthier check to make sure the bass is structurally sound as well. I was very fortunate with my bass. It is sound structurally; make sure yours is too before you spend money on it.
You can get a great bass out of one of these ebasses, it's just a combination of a good luthier, chance, and a little help from God, and believe me, I am not at all kidding about that. Good luck! I hope this goes as well or even better for you than it did for me!