to better configure a new pc build for AE, you need to figure some things out... you should look at cpu usage when you render or export a clip with the 'Detail Preserving Upscale' filter. if its not maxing all 4 cores (8 threads) then simply upgrading to a new cpu will have very little performance gain. recent versions of AE have removed the multi-frame processing feature (it was a work-around to get AE to use multiple cpu cores by launching multiple copies of AE in the background), and most of AE's functions are now limited to 2-4 cpu cores. if its not maxing all 4 cores (8 threads) you could try installing older versions of AE to find a version that has the 'Detail Preserving Upscale' filter and multi-processing feature/setting. if you find one, that may lower render/export times and would also allow using a computer with 6-8 core cpu for even better performance. if you are buying a pre-built computer you may only find an i7 6 core system for your listed budget and it may only be around 30% faster than your current system. it might also be slower if not using multi-processing in AE. a 6 core cpu system would also be a nice upgrade for premiere, even with HD timelines.
another alternative would be to use an AE render farm or at least a second computer dedicated to AE for these conversions. i'm not sure if render farms are still supported with newer versions of AE or not. if you cannot find an older version of AE with multi-processing and the 'Detail Preserving Upscale' filter, multiple computers may be the only way to get the AE conversion alot done faster.
another possible solution might be using a hardware based sd to hd converter that can do the conversion in real time. it might require an expensive broadcast level converter to get similar or better results than AE's filter. some of the hardware converters will have extra features like noise reduction and de-interlacing and more. i haven't used one of these before, but some from blackmagic appear to be within your budget. however they appear to need a thunderbolt connection or possibly extra blackmagic hardware along with the converter. so depending on what is needed, it may or may not be in your listed budget. you might have to research hardware converters and/or contact any video specialty shops near you to determine what equipment you would need. i don't know anything about this shop, but dvc.uk.com might be able to help as they sell video editing systems and various hardware, including the blackmagic converters.
if you only have a certain amount of footage that needs to be converted and then you will not need to do any more converting or very little, you might look into renting computers to convert with AE, or possibly renting equipment for hardware conversion.
Many thanks for the info RoninEdits.
I checked the CPU usage it was only showing 25% CPU used and only 4 out of the 8 being used.
I went and downgraded to AE CC 2014 and tried again and it now shows all cores being used at around between 55% - 75% which has halved the render time. Is there any way of still further increasing the CPU usage by changing anything in Premiere or After Effects?
just to be clear on your workflow, you should be doing these conversions in AE and then bringing in the new media to premiere after that is done. you can try using cineform or dnxhd mxf as the export codec from AE and see if one performs faster. both should be lite on cpu usage, but the cineform should use the gtx 970 to help speed it up a bit. also depending on which color correction fx you are using, it might be using the cpu and slowing things down. you might also try without any color corrections to see how much faster it goes and if its alot faster just save color corrections for premiere.
in after effects there are several settings to the multi-processing, that will control how many cpu cores are being used and how much ram each one can get. basically it controls how many background copies of AE will be launched and how much memory each instance can have. you can experiment with different core counts and memory allocation to see if some combination works faster. if you find that it runs alot faster with alot of memory per cpu core, then adding more memory might allow for more cores to run that higher memory setting and get a little more performance.
if the footage you are converting is only 8bit, then you may want to make sure the AE project and export settings are all set to use 8bit as well. any 16bit settings in there will have a big performance hit.