I would get a new psu as adapters are just another failure point.

inadub
Can you elaborate a bit more? From what I can tell, the only difference between the 6 and the 8 pin is two additional grounds? Is that accurate do you know? Most people have suggested that these connectors are bad.. but nobody really has any bad stories/experience or reasons. Others say they have been using them for years and no problems. So I am trying to find some info on what the issue "could be" and why it would happen. Especially if it is only to run a GPU fan which is how I would be using. 

Current carrying capacity is reduced when using an adapter. If a connection is loose, you could damage your hardware, or start a fire under heavy load.

It definitely handles more than just the fan.

No problem.

Me, I wouldn't worry at all about using a 6pin-to-8pin adapter with that card.

A GTX 1660 Ti is a lower-powered 120W card..The PCIe slot itself is rated for 75W..A 6pin PCIe supplemental power connector is rated for 75W..An 8pin PCIe supplemental power connector is rated for 150W..The 6 and 8 pin PCIe supplemental power connectors are for providing additional power over and above the 75W the card can get from the PCIe slot.

120W (card) minus 75W (from PCIe slot) equals 45W that would be needed for the PCIe supplemental power connector to provide/handle..The 6pin 75W rating is 30W more than the 45W the card could get from it, safe with no overclocking/overvolting the card.

There's other options too, such as Dual 6pin-to-8pin and Dual Molex/Perif-to-8pin and Dual SATA-to-8pin adapters that are widely available.

You need to be sure that a standard PSU would even fit in and be compatible with a Dell XPS 8900 if you're thinking about getting a better PSU..Prebuilts like that many times take a proprietary PSU and a normal ATX PSU won't work..You can check on that yourself..You might have no other option than to use an adapter.