>>1800897>>1800881Jumping in on this, I wonder how your posture is? Are you straining to reach the brakes? Your saddle is relatively low and your brakes are about far forward as they could possibly be, and in a funky spot on the bars. But to your question, if that's a good position on the bike for you, then I agree you'd definitely get some benefit by moving to better pads with holders - those one piece pads are never as good and they look old too.
>>1801069>>1801088There looks to be a big radial hop in your wheel I'd worry about first - back all the nipples off a bit, focus on addressing on that hop first, then get spokes tensioned evenly and then you can come back to that last little bit of lateral play. Also, if your rim has had some hard knocks in the past, you may not be able to get it perfect.