Still doesn't sound exactly like a Rickenbacker, even with the cartoony EQ and drive settings to give it the best shot at it. If you buy a Chinabacker and then piss money up a wall buying real Rickenbacker pickups to install in the thing then you have no financial sense.
A cool idea, but who shells out for a Babicz bridge and then makes a pickguard out of printer paper? The idea of a crossover P/rick has always appealed. My P bass is much more comfortable than my Rick, and has a nice grunt and heft to it versus the slightly more brittle quality of the Rick.
I used to think Rickenbacker basses were out-of-reach levels of expensive. I then figured out how to budget my finances and stash money away. I couldn't buy a 4003 overnight, but I could after ten months of saving and ring-fencing enough money, and sacrificing a bit of savings I might have used elsewhere. It delayed the purchase of my first car, for example.
Americans have this easiest of all, as Ricks are cheaper over there. Stash away $100 a month and after a year you have a $1200 chunk that will get you a nice used 4003. No Rick bass tomorrow, but don't impulse buy your next three $400 basses and see where that gets you.
If the 4003 is the bass you want then you won't feel sad about spending that $1200 after a few months. I went balls-out and bought a Kitchenaid mixer a few years ago when I pretty much could only barely afford to do so. The thing is still pride of place in my kitchen, and I still use it regularly. I've forgotten the financial shock of the purchase now, as the mixer has proven to be so useful and robust.