Here's a completely different perspective. Since it is a parsonage and they don't own it, and have been told to leave the countertops, and there is a green sink and a green range let's work with the green to bring them some harmony and warmth. Green is a neutral that really is very versatile.

I say - don't waste your time messing with the brick either - the effort and money you would spend on the brick could be used on the things that will make a bigger difference and that you can take with you (new curtains) - painted brick with semi-gloss that is easy to scrub will add some modern style here with the standard fixtures. Finding the right pretty linen for walls and buff tone for all the brick will add so much to your room. Start with the simple / most inexpensive solution.
For the walls - BM Manchester tan is ideal http://www.benjaminmoore.com/en-us/paint-color/manchestertan it is shown with your green tone - it will sing harmony
For the brick - BM Baffin Island http://www.benjaminmoore.com/en-us/paint-color/baffinisland
a bit deeper / another one to test is bm glacial till
those both work well with manchester tan and either one will look good next to the white appliances and the green top / range

Ignore the places where the brick is coming apart / don't repair, just paint - it won't be noticeable and is a lot easier than reworking it. Get some good epoxy glue and glue back anything that is dangling but otherwise ignore it. It adds a lot of charm to the room because of the arch and you will spend more than you would for new countertops and new range to try and rework something over the hood / build up the drywall column behind the oven. There you would need tile - all that gets expensive - tearing that out is a lot more complicated than you think.

Painting the cabinets is a big job. Ask at bm for a special paint additive for this - One advantage of dark wood tones is that they clean up really well. You could put some new hardware on them and live with them a while first, and then, if you still want to paint them, paint them a creamy off-white - bm palace white is also shown with your green tone and resonates perfectly with the manchester tan and baffin tones. Don't go stark white - the green you have has yellow undertones, so everything that you use is best when it also has yellow undertones - it also adds a lot of light reflectivity.

Finally, take a darker color tone from the green avocado - a deep mossy green like bm shady lane - get a quart and paint some chairs for the eating area, or a craigslist find sideboard or storage piece to bring the green in a deeper, more flexible shade into the room elsewhere - then the green tops will feel curated. The result will be mod with dark cabinets, even brighter with the light cabinets.

If you have any budget left, use it for vinyl wood plank look flooring you just put on top (99 cents a square foot) or if you have wood next room, cork flooring. They both wear well / can be budget friendly options if you shop the sales.