Mortgage and debt question

Just wanted a vibe check because what my dad heard from a mortgage broker seems crazy to me.

Here’s the basic situation:

Me, early career academic with a professional degree

$160k annual income currently

$100k on a professional line of credit. $200k valuation with prime - 0.25% interest. Enters repayment in August but they have offered to convert it to a personal LOC at the same valuation. Currently just paying interest.

$15k in savings

$30k in investments

My dad, who would be on a prospective mortgage and is providing a $200k down payment

Retired

$2.5 million in investments

Prospective house would be around $800k-$1 mil

My dad talked to a mortgage broker and they said we would never qualify for that mortgage because 1) my LOC debt and 2) I would be moving to a new faculty job and therefore would be in “probation” until I got tenure. Mortgage lenders would consider me to have zero income during that time.

That seems crazy to me??? I know several early career academics that have mortgages before they got tenure, and I also have a hard time believing we would be denied for a $600k mortgage backed by $2.5 mil in investments over $100k in debt. Please tell me this mortgage broker is insane lol

Also: should I pay down my LOC with my investments and savings? Only reason I haven’t is that I am only paying interest on it right now, so it seemed more financially sound to build up savings rather than pay down that debt, at least until it enters repayment.

Thanks Reddit 🥰