If you need a running, in car m62tub44, I am about to pull mine for an engine swap. 155k miles, light vanos rattle and the timing guides should be done in the next 20k miles. I assume the previous owner did them @ 100k but they never gave me paperwork to support that notion so best to be safe.
No codes and always serviced at bmw certified shops running full synthetic oil on every change.

I would stick with the tu44. Easier job rebuilding it than swapping in a b44 and dealing with electrical issues.
In my humble opinion. BTW, sorry the rig you bought had issues when you got it.

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'03 4.6is (the wife' s ride)