following coins between blockchains Question: is it possible to further obfuscate ownership/origin of bitcoins by trading it for another cryptocurrency at an exchange? (as it is easier to do this for large amounts than it is with cash)

Lets start with 10000 bitcoins. The point here is to make the size a large and conspicuous one.

You have 10000 bitcoin that you would like to obfuscate the origin of. Right now those 10000 bitcoins are at an address you control. The object here is to move around that value between addresses.

Just sending them to another address would have a record of all the addresses they were sent to.

Sending them to an exchange and back would still have the record as well as the exchange's records.

Even breaking it up into smaller transactions just makes it more tedious to follow the pieces but it is all still easily browsable using existing services.

But what if they were traded for another cryptocurrency at an exchange?

This gives you the initial transfer to the exchange, everyone and the exchange can see that. But then they are exchanged, probably nominally, on the exchange for a different crpytocurrency. A completely different blockchain. For someone doing an analysis on the trail of these coins, how would they be able to account for switching blockchains? Would it even be possible at all?

Going to a different blockchain, and even then going back to the bitcoin blockchain at a different address seems like an impossible thing to follow.

Is there a way to follow coins exchanged between blockchains? Is there a way to know that the owner of the 10,000 bitcoins exchanged them? since on the bitcoin blockchain, it will all have happened on the exchange and the coins will simply look like they have been broken up between addresses, but you wouldn't know that the original owner is no longer holding those coins at all.
If you want to hold bitcoins anonymously then the only thing you can easily do is a cash transaction.  In the good old days you could just have mined some, but that's not an option available to most people today.

To answer the specific question, the exchange will have records of the receiving and sending transactions, so if you consider them to be compromised then there is no additional security available in using an exchange regardless of if you are moving currency within a blockchain or  between blockchains.