eww yuck. I am not sure what to advise here. it could get messy quick. Best bet is likely to hunt done 6.1.62 if you can find it. Stick it in the dl folder and check the hash is correct. Beyond that you'll need more help than I can offer you at the moment.
That link shows version r28597-0425664679, which gives me different kernel hash when I compile a package. I used SNAPSHOT, which, obviously, was changed, and I can't find c60e9d1839 commit anymore...
Obviously, any SDK generated from a daily SNAPSHOT isn’t likely to be around after a day so if you insist on using 6.1.62 you’ll have to build it yourself.
Set up a build environment (clone, menuconfig to set a default .config using just Target/SubTarget/Profile and ensure Build the OpenWrt SDK is selected)
Access your Buildroot and point HEAD to original commit by git checkout c60e9d1839 (Verify by git log). Then just make, and wait for it to finish.
You should find linux-6.1.62.tar.xz in your dldirectory, and your sdk tarball in bin/targets/ixp4xx/generic/
Just out of curiosity, what’s the kernel hash you’re expecting?
And this is the hash: 821a13ca7003d3cef4249b9eaf1f7241
However, I'm afraid it's almost impossible to reproduce it. AFAIK hash depends on many things like kernel settings and code. That was quite experimental snapshot which I helped ixp4xx architecture maintainers with and they experimented with the code.