One of the advantages of using a template is that it's easier to refine the shape on thinner material - involving less elbow grease to get it to the correct shape. The router then transfers that shape accurately to the wood.
You have really answered your own question. Touch is about the most important sense in guitar building imho. Persevere with refining your shape by feeling the bumps and troughs, and looking at it from a distance, close up, in different lighting conditions. Something like a shinto rasp or dragon file can help to remove material quite quickly, followed by coarse sanding using a range of suitable blocks, and then maybe finer grits or cabinet scrapers. Try to keep the sides perpendicular to the top too (another advantage of templates + router) - it's very easy to drift away into an undercut or overcut.
I've used various things hanging around the garage for sanding blocks - from chunks of mdf to short lengths of copper pipe to drill bits to offcuts of beading. The way I do it is to sit down, grip the body between my knees and use both hands to guide the sanding block. Focus sanding on the bump initially, then blend it into the surrounding wood with progressively longer strokes (and repeat a lot), stopping every now again to feel it, usually with my eyes closed. Given enough patience and perseverance I'm sure you'll get it "right"
I think I have a photo of my favourite sanding "block" (a length of "D" shaped beading) on my phone - I'll edit this post and add it if I can find it