I'm afraid I don't know an easy way to do this, but I understand the frustration. It's something that is so easy using the CLI, but when you try and do it with SNMP the information is presented "back to front", so it is a long involved process of loading whole tables and then doing seraches.
I use CA Spectrum and I wrote a script to trace a MAC address through the network so that I could track down rogue hosts and errors in my model placements. I did it using exactly the same steps as you suggest. That is, I go to the router, download its ARP cache to look up the IP address I am interested in and get the VLAN. Then starting at the VLAN root, I go to each switch in turn, laboriously download its forwarding table using CommunityString@VLAN, get the ifindex of the next hop port, etc. etc.
The only thing I can suggest is to search the MIB specifications to se if there any shortcuts. If you find any, then please let me know .
We are pleased to announce availability of Beta software for 16.6.3. 16.6.3 will be the second rebuild on the 16.6 release train targeted towards Catalyst 9500/9400/9300/3850/3650 switching platforms. We are looking for early feedback from custome...