It's an interesting one and having used exercise myself for similar reasons I understand your dilemma a lot. I do think the tiredness may just be related to the redundancy mindset, but, equally, the repetition of cycling local roads may not help your boredom/need to 'take your mind of things' unless you have the right perspective for it.
Here are some suggestions to consider.
Volunteer - it doesn't matter what, or for how long, but volunteer for a day/2 days/more in a week. I had a time back in my early twenties where I was in a very difficult life situation and I wasn't equipped mentally back then to deal with it. I got chronic fatigue and was unable to function all that well. So I volunteered in a charity shop a few afternoons a week. It was hilarious, rather like the League of Gentlemen, with a mix of lovely and angry old ladies to work with (all of who made me smile in one way or another, either with them or at them!) and the time always passed quickly. There are a number of options out your way - how about the museum/library/scout movement/church(you don't have to be a believer to help others through the church)/school (my Mum volunteered at my Junior School throughout my childhood and well beyond because my dad would never let her work - it gave her a purpose and the kids all loved her being there, except me haha) etc etc
Ride your MTB instead of the roadie. Really get up into the hills. If it's lack of rest that's making you tired this may make it worse though.
Stop immediately paying attention to your speed on the bike. You mention you are going slower. Who cares? Just stop right now even thinking about it. For the purposes of curing the blues it doesn't matter at all. You could go out and ride at 10 mph every day as long as it's getting you out and at that speed you really won't be 'doing too much'
Short term foster - children or animals
Have a look into Mindfulness. There are numerous sources out there. I would recommend 'Taming the Mind' by Ruby Wax as a starter.