Well, I stand corrected they did use wood binding. I wonder if they only had guitar width fingerboards and used cutoffs to make it wide enough for bass...Cool. I still do not recommend removing the binding, and re binding it with plastic. But it is a $30 bass and you seem to have the passion for it...
I actually wrote out instructions for how to do this and came to my senses. I am not going to tell you how to replace the binding. I am not calling myself a master repairman by any means but even I would be hesitant on doing that. The best way I can think of is removing the fret board with a heating block remove the binding at the same time. That is a tricky thing to do and the likely hood of you warping the fingerboard is very high if you haven't done it before. Besides that you would need a bunch of clamps, cauls, files, hand planes (or a lot of block sanding)... This is a long winded way of saying I do not recommend you doing it. If you fully realize the risk and want to do it anyway (like many of us luthiers do) I will give you the steps to get r done.
Looking at the pics you did a decent job of controlling chip out

however you got a little gorilla handed with the down force of the fret puller. all those dents of from the flush cutter, good thing is that it doesn't appear that you cut any wood fibers so not only could you steam those out if you wanted to and you are going to be radiusing the fb anyway. Start with 120 grit on the block and only go to 220 then 320. For raw wood you don't want to go higher than that finish has a hard time sticking. for finish you go as high in grits you got.
You can also fix the fb edge when radius sanding the fb. Depending on how much you take off, the din will have less wood to look off. additionally you can mix the dust from the fb with high viscosity superglue shape it on the edge of the fb and re shape it kind of like wood putty but an exact match. I appreciate the attitude of intended precision. if you wanted to be super pro - use a chisel to make a flat even edge and glue/clamp a small piece of rosewood to it and shape the glued on chip to be flush with the side and top (radiused) parts of the fb. If you don't build it may be a trick to find a small piece of rosewood...especially in a matching grain and color.
When radius sanding clamp down the work piece so all you energy is going into sanding not being a human vice.
Use a straight edge to see how flat you can get you fb, by removing the truss rod tension a little bit of back bow is a good thing. Ideally you want something to support the headstock and neck so it doesn't move when sanding. When you apply force down the neck will want to give a little.
Get a with colored pencil to mark up the fingerboard to check for consistency in sanding. Literally squiggle white lines all across the board between each vacuuming.
Be sure to visually line up the block on the center line and do not go crooked with each pass. I would recommend to sand just to the 95% mark of removing the chip outs and making the fb "perfectly level".
Install the blocks knock them down as much as you can first with a flat block being careful not to sand into the fb making flat spots (undoing the work you just did). the return with the radius block until flush and getting that last 5 % with 120, do as many passes with 220 as needed to remove the 120 scratch lines then with 320.
As stated before be sure to have a vacuum handy to remove dust from the block and board. The oily nature of the rosewood will start to clump up in spots on the sand paper cause its own micro scratches and imperfections. Also for checking your self with the radius gauges constantly.
Did you use a metal file on the fret slots? perhaps to knock down the little bit of chip out you had? I see chatter lines
