Yes, you can definitely field a Tiger I Co. in Late War 4e.
And I'm sure you can get those Engineers & Panthers into the list. It might take some fiddling around & squeezing them into the support section. Or just running a 2nd detachment of some sort. But I'm pretty sure it can be done.
I'm not sure of the pts this would entail, but as several of the
LW German/Axis books specifically mention lists for Tiger formations, a good chunk of this will fit into the standard 100pt lists.
The King Tiger? I don't think that's made a return yet for 4e. :( Looking through the
FW site I don't even see the model listed anymore.
How to get lower skilled Tigers?
1) I don't know if you can do that in any of the actual German books. It
might be an option in one of the decks of Command Cards. I know
other forces have cards that modify stats to make specific units, so maybe? I just don't know all the German cards.
2) How do you feel about running your Tigers as Romanians rules-wise? Because in the Bagration: Axis-allies book it allows you to play a Romanian Tiger Co. And they can use Panthers. I can't imagine that the Romanians moral/skill stats are as good as actual Germans.
https://www.flamesofwar.com/hobby.aspx?art_id=7241
Hope that helps & you can get your tanks back on the table.