cool.. thanks for the Pics! I'd say a nice set of Alivio Derailleurs would be great, Or you could step up another notch to Deore for a few more dollars. Most Absolute 3.0 came with Acera level ders, just a heads up... Replacing the Control cables will be wise at this point too.. re-using old shift cables is a literal Pain... the frayed ends love to pierce finger skin.
Personally, i'd go with the Alivios.... they look great and are a bit less spendy..
in case it comes up.. the shifters are "MTB"... Front derailleurs have a different pull Ration between Road and MTB types.. so be aware. Alivio and Deore are MTB ratio.. as are Altus and Acera.
and yes.. New Alivio, and Deore "9 speed", derailleurs work fine with 7 or 8 speed setups... it's the Shifters that work differently, not the Derailleurs.
That Freewheel (rear gears) looks new... a bonus. is the chain also recently new? when swapping rear derailleurs, a longer, or possibly shortening the chain will be needed. Ask for help and watch a few youtubes on chain setup,if you've not done them much..... i use the "Small/Small" method, and always have. I buy chains in bulk... sold probably 75 or so last year.
now.. grab a rag and some penetrating oil, and Start Cleaning that Fuji ! A clean bike is a lot funner to work on
Tip: Pressure Washers Push Water INTO BEARINGS.