You should be able to. There are track adaptors which will take a basic cord for a pendant or a plug in. I've linked to the plug in version. Look for EP 814. If you go to the next page, the EP 815 can work as well. You'll just have to cut the actual plug off and wire your fixture directly into the 815. This one is nice since there's a ring to support the weight of the fixture. I don't know if your light has a support cable or not. You obviously don't want it hanging just from the plug with no support. Here is a link that might be useful: Plug in track adaptor

I disagree that the pin-type fluorescent bulbs have "uglier" light than the screw-in fluorescent bulbs. I think it is about the same. I still prefer the look of incandescent lighting, but here in California we are required to use fluorescent or other energy efficient lighting for over 50% of our total wattage in kitchens. I also feel a moral obligation to conserve where I can. If you get the "warm white" color spectrum bulbs, they are okay. In my kitchen, I have mostIy 5" diameter can lights with 26 watts each. They take the pin-type bulbs. I would recommend them. I would definitely not go lower to the 13 watt fixtures. I do have a 5" can over the sink that uses a PAR bulb, and it puts out MUCH more light. I wasn't happy with the amount of light I got over the sink with even a 26 watt fluorescent bulb. The advantage of using 13 watt fluorescents is that you can use a 4" can, but then you will just need more of them. You trade off smaller holes for the swiss cheese look, so I don't think it is worth it. In my office, where I am usually in a seated position, I put in 6" can lights that take screw-in fluorescents. I am happy enough with them. There are fluorescents that dim, but they usually dim to an ugly shade. Think about whether you will want to dim your pendant lights over your island. Also, with a pin-type fixture, you only have one option of wattage to put in it. I don't see any advantage at all for you in choosing island lights that take the pin-type fluorescent bulb. You will be paying more and limiting your options. The fluorescent bulbs do use mercury and may be replaced some day with an even better technology. I would just buy regular fixtures and put fluorescent lights in them.

A shop that repairs lighting fixtures will probably have a spool of the cord. Replace the entire cord with a piece that is long enough. Make sure to pay attention to how the cord is secured at both ends.

For heavens sake, just get something that HAS the adaptor feature. There are many. Just a few below. [https://www.houzz.com/products/access-lighting-pendant-brushed-steel-prvw-vr~26998985[(https://www.houzz.com/products/access-lighting-pendant-brushed-steel-prvw-vr~26998985) [https://www.houzz.com/products/k-single-pendant-white-sleeve-prvw-vr~38110130[(https://www.houzz.com/products/k-single-pendant-white-sleeve-prvw-vr~38110130) [https://www.houzz.com/products/dainolite-1-light-pendant-steel-silver-sleeve-prvw-vr~87830487[(https://www.houzz.com/products/dainolite-1-light-pendant-steel-silver-sleeve-prvw-vr~87830487) or get with this:https://www.perigold.com/ARTERIORS-Home-Sloped-Ceiling-Adapter-PIVOT-100-PIVOT-101-L269-K~ARN3595.html?refid=GX195890756601-ARN3595_12549987&device=c&ptid=314658904231&targetid=pla-314658904231&PiID%5B%5D=12549987&gclid=EAIaIQobChMIiKv1nK_11wIVQxuBCh2w4AfNEAkYCiABEgIVpPD_BwE