I'm sure that there are people that know a whole lot more about everything going on than we do and won't listen to any suggestions here even if they were better ideas.
As I was reading the second article, I had an idea. If Capitol Police were able to get permission to use one of the DoD systems, see if they could purchase radios from (guess here) Motorola to use on one of those systems. Have an agreement with Motorola that when they have their own system in place, they can trade in those radios for ones that would work on their system if they were not already compatible. Once their new system is almost ready or in the process of replacing\reprogramming the radios, have patches to the DoD site's TGs until all is complete.
This would allow them to have a better system right now. It would not meet all their needs totally but would be a lot better and more secure than what they have now. It would also make use of the funds they might have now and kinda make a step towards the new system without the risk losing the funding.