As far as I am concerned the bottleneck here, and the easiest solution is one of 3 things. I've omitted any parkway stations based on cost.
1) Build some sidings north of BDM for trains that will reverse. Just keep them at BDM for the duration of picking up passengers (shocker).
This is a very cost effective solution and north of BDM there is great road connectivity as you can easily access by road from Bromham. Drivers may have to cross the tracks if the sidings are on the slow side. In fact the Northampton junction signal box access (the access is there, the signal box is not since 1965 or something) at Lower Farm Road now has temporary OHLE equipment there and can be re-purposed.
2) Make a through road at Bedford for freight. Not my preferred option.
As previously stated I would knock away Platform 3 in part, move the P3 rail track close to P2 and build a platform on the up fast. This would allow only 2 terminators at BDM on current P1 and P2, would allow a through freight road like at Northampton. The upside is that East Midlands trains would stop on the fast. Currently all southbound EMT cross to the slows since there is no up platform on the fast at BDM. This is currently adding to the bottleneck.
3) Create a freight loop north of Bedford and south of Bedford. Whilst freight traffic will not benefit on their timings since they will inevitably park, all through roads north and south of Bedford would be freed up for passenger traffic for the duration of the bottleneck. The bottleneck would be shorter under this format so things would be slightly quicker.
Lets not forget passenger traffic does currently suffer. EMT trains approaching from the north quite often slow down to a crawl between Sharnbrook and Bedford north junction due to amber/reds. From the south its not too bad since BDM has a P4 on the down fast. Had that not been there Thameslink wouldn't be able to do what they are currently doing. P4 has actually enabled more terminating trains at BDM because EMT would simply not have access to any platforms at all when all 3 current platforms are filled in peak times by Thameslink trains. And on that subject why the hell does BDM need 3 Thameslink terminators in platforms at the same time? Its simply greedy and the passenger uptake at BDM trickle feeds onto the trains because they are parked for so long as previously stated. If the passengers know the time of the train they can accumulate on platforms just like they do for EMT.
If Wixams goes ahead, a middle road loop would be beneficial. If they are going to build it, might as well take the pressure away from other areas. A cheaper option would be to join the Elstow cement sidings to the main line on both ends. Its really long looks like a simple join up. However, I don't know if its private land. Those tracks are certainly being wasted when they are empty 95% of the time.
As for the parking situation. Oh, thats a bad one. Bromham road bridge rebuild is going to eat at that for a duration. I can hear the cries now whilst some crane equipment is eating up 50 spaces. Which is similar to what might take effect when 1a becomes a through platform. You could build a multi storey, but not without completely closing huge sections of the car park for a long duration.
Thats why BDM needs a complete rethink from scratch. All these expensive upgrades only provide a 5% increase in capacity in certain areas whilst neglecting all other concerns as well. If you bite the bullet and give BDM what it really needs its more expensive, but the provision for capacity increase is 100%. Which should buy you many years and if a new station had a huge car park the station could be built bigger down the road.
Lastly, all these problems are current day. EWR is far away and will only increase the problem. Any freight using the line will pass through P1 or P2, shock horror. By 2025 when the problem is a crisis, I bet thousands of new homes are built either sides of the tracks making any of what we are talking about totally impossible. There is a difference between expensive, and impossible.
Could I argue that someone at some point thought to put 8 platforms at Nuneaton. Built a whole junction network of track where lots of railways all meet. The population is quite low and there isn't much business there. You don't even get any fast trains to London from there. Where as Bedford, wanting to be a rail network junction only has 4 platforms, does have fast trains to London and completely isolated by bridges and any expansion possibilities beyond doing a little. I would say the customers will suffer in the long run. Profits will be high, customer service will be terrible.
I've edited this several times.
One edit was Elstow cement sidings being used as a loop. Currently one end is attached to the mainline. If both ends were connected -