Husband in denial about his parents; how do I get him onboard?

Why would you and your H pay fines for your in-laws? Their money should be funding any leases, AL, and everything else.

Two months is enough, but maybe ask landlord for a month extension.

Maybe you should start by reading a sort of primer we old time posters have put together. Its in the discussion section and titled "New Posters, read this first". Have your husband read it too.
https://www.agingcare.com/discussions/new-posters-read-this-460522.htm?orderby=recent
Are your in laws willing to move? Do they have the funds to pay for AL?

If so, that's great. Make sure you have POA for health and finances for them both.

Are they capable of packing their essentials, as though they are going on a month-long cruise? That will help with essential clothing and such. Next, off season clothing in some bins for storage.

If you've picked the place they are going to, make a diagram and figure out what furniture they can take. We found it easier when my mom moved to buy new, inexpensive stuff from Bob's rather than to move her furniture.

If this is really a very daunting task, hire movers to pack the rest and put it in storage so that you have more time to sort stuff.

The storage unit that your husband thinks can't be emptied in 2 months - is it part of the apartment deal? Is that why he thinks the move can't be done before the lease is up? Most towns and cities have heaps of private storage units, in rows looking like garages. If the existing storage is linked to the lease, hire one of the private ones for a year and shift everything into it. It has to be cheaper than renewing the apartment lease.

What is in the storage unit? If it doesn't fit in their apartment now, how will it fit in an assisted living apartment? Maybe time to downsize further?

The distance between 'starting to talk about it' & 'done, moved' varies a lot.

My friend's folks, talked, downsized & moved in within a few months. There were younger retirees & once decided, were highly motivated to start the next part of their life.

I'm not feeling the vibe your in-laws are there. Or your DH.

So you can nudge then along maybe... Are they looking for someone to take charge? Or someone to offload all the work onto? Be wary!!

Or wait. Pull back from whatever you do to support their *independance*. Let it fall on your Husband. More than one Husband, when that happens starts yelling I can't do all this!! And the denial just fades away...

If your In Laws are already mentioning going to an Assisted Living, then do some research and find a couple nice places and take your Inlaws to visit and if your husband wants to go along fine if not ho without him.

Will their Insurance cover the bill or do they have money saved for this?

Your husband might be waiting for you to ask him about his parents moving in with ya'll.

Your in laws are on board, they’ve already researched and found a place they like. That’s wonderful.
Next step signing leases etc.
Third step packing and moving.
If husband wants to help, even better- if not, at least in laws have you.
Signing leases is fine, (I’m assuming they have no dementia, that they don’t NEED their sons permission.)
packing and moving can always be bought if it comes down to that. Are their friends or club members who could assist, if professionals are too expensive ?
if they’ve not touched items in storage 3 years are they more detached from the items now-can they donate to a shelter?

I am an only child, 73 and not in great shape. My mom (95) was living on her own in her condo until she had a stroke. In the space of three weeks (1 in hospital 2 in rehab) I found a nearby assisted living, got her condo sold, moved her furniture to the ALF, distributed or sold remaining furniture, changed over her phone service and still managed to visit her regularly. I am not saying this to pat myself on the back but rather to say it CAN be done. Hard? Yes! But you just need to grab the bull by the horns and go! Maybe if you started a list of things that needed to be done it would help your husband to see more clearly. He could just be overwhelmed by the enormity of it all. I kept a notebook with different sections. When I would meet with the realtor that went into one section that I could refer to if needed. All progress was kept together and that way it helped minimize my confusion. Good luck!

What is there to discuss?

Take your in-laws to sign up for the AL. Schedule a move date and inform your husband that his services are needed on xyz dates.

You can go through the storage and take any photos and family memorabilia then be present when the estate sale company moves and inventories everything to ensure that you have not missed anything.

It is okay to do this for your husband's parents, they need help daily and he is dropping the ball, pick it up and go with it. No one needs his permission to do this and they don't really need his help because everything can be hired.
The longer you wait for him the greater the chance that something happens and creates an emergency. Get them moved!