Hi Drugpickle
your temps are not that bad , better airflow will certainly help and cable management is a must for good airflow ,
when you add more fans to your case try to get positive air pressure this is done by more intake fans than exhaust , this will help reduce dust in your case, if you must have the case on the carpet then i would turn your PSU upside down so it draws air from inside the case rather than underneath the case on the carpet . A good aftermarket cpu cooler is a good idea to help lower temps dont forget to apply thermal compound.
Also check your case for dust and blow out with a can of compressed air , if your gpu heatsink gets clogged with dust it cannot cool efficiently , it sounds like you have the right idea and i hope it all goes well for you , let us know if your temps improve after this