You have such a requirement mix of fish in there! While African cichlids like that high pH & DH, Cardinal Tetras are at the other end of the spectrum - low pH & DH. I would slowly add Biphosphate and try to bring the pH down to about 6.8. What is your water Hardness? Mollys and Zebras can tolerate the current conditions, and so would any of the brackish fish, like Bumble Bee Gobies, Glass Cats, Archer fish,....

Most tropicals can adjust to different ph levels if it's done very slowly. Not sure if the cardinals can go to 8 but you might try to alter the ph to match the stores water with chemicals, put the cardinals in and let the water slowly drift back to tap water levels. Trying to adjust the ph all the time takes a lot of fun out of the hobby. You could get a reverse osmosis filter but its pricy and slow. Large amounts of peat in the filter may also help. Ask the store what their tap water's ph is and if they adjust it.

One problem is that bumble bee gobies get very aggresive after they mature. After about 6-9 months they will maul anything they can get their teeth into. I have never kept them, but always wanted to. I did the research and from sharing with others experiences, they are better suited to be kept alone. The good news is a 10G tank will do fine for them. They don't get very big.
Your biggest trouble is your ammonia! It seems you are still in your cycle stage. The stress of the first stage of the nitrogen cycle is your worse enemy right now. Ammonia is also more toxic the higher the pH. Besides that fact, don't worry too much about the pH unless you are planning on getting more delicate fish (like Discus). Although cardinal and neon tetras "do better" in more acidic water, doesn't mean you cant keep them at all. Mostly it may shorten their life span (or not) and breeding will be harder or near impossible. My experience with peat is very little pH reduction and tea colored water. The water is no big deal if you don't mind it. The fish certainly wont. For the size of your tank the amount of any pH down and similar phosphate based products will be very expensive. Your pH will fluctuate up and down and as James said in not so many words a major PITA. Another downfall of these products is that the phosphates usually cause green water algae.
To answer your question though the most efficient way to lower and stabilize your pH would be compressed CO2 injection. This would run you a cost of about $200 for a automatic CO2 injection, no brainer system. Try to get a used one from ebay or other auctions, even new stuff on ebay is reasonable. CO2 is also invaluable to live plants if you ever go that route. If you ever go with salt water it can be used with a calcium reactor for corals.
But for right now, I would focus on monitoring your ammonia and keeping it as low as you can. .25 for cycling is good, try to keep it under 1.0 ppm until nitrites show. Nitrites will spike up in the second stage, but you can block their toxicity with salt or a good water conditioner.
Hope this helped.

Good points woeisme, I didn't notice the ammo reading. I have a 240 gal sw tank and it took months to cycle. Hold off on any sensitive fish [like cardinals] until the cycle is complete. A school of 30 or more cardinals would look great. I have about 12 in my 150gal and they usually school. Whats the demensions on your 240? Mine is 8'x2'x2'.

Thanks for the feedback. My tank is a cube 48L x 42W x 39H. It is well planted with plastic and silk plants and has rock stacks for plenty of hiding places. I plan to introduce angelfish once things have settled in and had some grow time. So far, the bumblebee gobies have been pretty calm. I am relying on the cover for the others to escape the bees' territory. The .25 ammonia reading is the lowest reading above 0 on my test kit. I did change out the cannister filter after the last cardinal die out. Maybe I tripped the cycle. I did find that 2 cardinals are still alive.

Brian

I dont know what type of filter media you use but just rinse out the sponges with a bucket of aquarium water, or tepid tap water if you have a private well (no chlorine or chloramine). If it is just a spike after you have cycled then it will have gone away by now. Don't worry about having a totally sterile environment. It is better off with a little "dirt". If you feel the need to remove some "impurities" after a fish death do a PWC and just change the activated carbon in the filter. Never change all your filter media at once. Just part of it one week then the other part(s) the next. This way all the bacteria colonies wont be removed. Angels and gobies sound nice together, but I think you'll have alot of fish fights in the future. It may be easier to stick with fish that are compatible. Actually, rift lake cichlids are awesome. Lot's of color and it seems your water supply won't need much altering. Also, one note on pH. Sometimes the gravel you selected or certain aquarium decorations spike the pH. I had a gravel that spiked my pH up .8 . Also, seashells and ceramic decorations will cause a spike. Is your tap water (after aerating aday) also high?