announcing IPs with BGP

No idea at all, but I’m missing too much information, e.g. whether the public address you test from is currently runing at a pppoe client or at a device connected to the 'Tik’s LAN, whether only the browsing is slow or even ping round-trip delay… there well can be some throttling at the ISP because they forgot to apply the policy on the public addresses…
So first thing I’d do would be to compare apples to apples, have a private IP NATed to the link IP you get from the ISP and one of those public ones of yours with no NAT handling both connected the same way (e.g., assigned to a PPPoE client) and check the download speed and ping RTT for both. Then, I would extend the NAT so that it would translate also that public address of yours to the link IP you get from the ISP and check whether that changes the speed or not. If it does, either the ISP is throttling the traffic to those addresses, or the network path between the remote endpoint of the connection and the ISP’s network differs depending on the address used at your end because the BGP propagates a different path. A traceroute from the same remote endpoint to both the link IP and one of yours should reveal this. If the traceroute shows the same route for both, ask the ISP for explanation.