First of all, I want to say that Brooks Laich is my favourite player of all who have ever worn the Caps jersey. So I'm more than a little biased.
Second, this proposals are more about offseason and not deadline because I'd like to see more of Eric Fehr to see if he sticks with the Caps.
The rationale behind the proposals is:
If we go with three scoring lines, then it's pretty clear that you don't have more than 4 "grinder spots" in that top-9 and we have Fehr, Ward, Brouwer and Chimera who do that job well. Of all mentioned, Laich's value is the highest (except for maybe Brouwer, but Laich's older and is paid more.
If we go with two, then Beagle does the job perfectly as a third line center, he's been great lately. And then I don't see where Laich fits. Even though I am, as I said, a big fan of his. Playing him in a 4th line role would be a disrespect to such a great player like him. Playing Beagle there would be an even bigger disrespect to the progress he made since cracking Caps line-up full time.
So, the idea is to trade Brooks Laich for a FO-winning/defensive-minded #4C on a cheap contract (preferrably not expiring soon) and a first-round pick. Additional piece from the Caps side, like a fourth-round pick or some C-rated prospect (or both I think) could be added.
I do not know if these teams need a third-line center. If yours does, post what you have to offer.
Among fourth line centers I liked:
If JT Miller doesn't stick in the NHL how about Skjei/McIlrath + Boyle? And we give you a 3rd to keep 33% salary?
Forgot to mention in OP that retaining salary is not an option because we have many players requiring raises next summer. Would you rather part with Skjei or McIlrath than first-round pick? I've heard they're bad but are they really that bad?
Do you have problems with how our bottom-6 plays right now? I don't. It's doing great. PK could get better, but it's more of defensemen problem. Hendricks/Beagle, Brouwer/Backstrom, Crabb/Ward do pretty well.
If I were Washington, I'd hold onto Laich. His absence is a big reason why the team has struggled out of the gate. Yes, new coach and not too much time to get the system in place is another major reason, but which what Laich brings to the table, he could have turned around a few of those one-goal losses into ties or even wins. Keep him. Good solid players like him you don't discard.