Second the recommendation for a better cooler. Yeti makes much better coolers than Igloo if at a much higher price. Rtic makes similarly excellent coolers, but at a somewhat lower cost.
Haven’t seen that it’s mentioned, but I’ve had limited success with dry ice.
I suspect most people aren’t as hard on coolers as I am. Story: I bought an Igloo 80 cooler on sale for about $150. Over the next four or five years I replaced hinges, latches, handles, and hold-down rings as they failed. The total cost was well over $600 by the time the case failed due to UV deterioration. My Yeti 72 cost about $400. That’s a lot for a cooler. It is now about eight years old. Total cost since purchase is a squirt of Armor-all on a rag to wipe over the rubber latches about once a year. When I remember. That’s value for money to me.
Now the way I use coolers is NOT what Gwenn faces. I’m not suggesting she have spent more money. For those who boat or hunt or fish or camp a LOT I think the cost of a Yeti is cheaper in the long run. That’s before you consider the impact on your plans of having to go get ice twice as often with a less well insulated cooler.
I am a happy Yeti customer. I sent my story to them and they sent me a thank you letter. I’ve never received any compensation for sharing it.
Better cooler for sure, but on your original question, i prefer the blue feel packs over ice (the bigger/longer, the better). I just dislike the moisture that will seepo into so many things as the ice melts. Plus it will just make that cooler all the more difficult to move and empty unless you have one that drains at the bottom.
As another alternative-how about dry ice? You can sometimes find vendors who sell them to you if you are packing perishable goods (we’ve had luck when we bring lobsters to guests far away). Just way colder, so it’ll last longer. Just make sure, you’re not trapped in the car without the window open for long times with that.
Edit: Just saw that won’t work for insulin. 
What if the dry ice itself was insulated in a layer or two…? If that’s even an option you want to consider., Of course.
