Best way to reorder long list of items

I'm currently working on reordering items in a list. The tricky part though is that I need to be able to reorder up to 100 items. I have some solutions in mind but I the design will break once it tackles probably more than 20 items that would lead to a very bad experience for users. Would love to get your thoughts and ideas how to be able to do reordering of a long list of items.

Some solutions I thought:

Option 1: Drag and Drop to reoder items

As you can see, it would be so hard to drag the items up to 100th. Scrolling would be a pain as well. It would be great if you can share your thoughts for better ways to use drag and drop.

Option 2: Arrow Button Up and Down to reorder items

Reordering works here when you click the arrow up and down. The issue here though is when you reorder that items that are too far like if you want to add Item 98 to Item 2.

Quick solution to solve it though is through pagination where we only show 10 items per page at a time. Reordering just happens within that though. So the pain is when you reorder items from other pages.

Option 3: Using dropdown to select which position the item

Would be very happy to hear your solutions. Thanks!

Update: I'd like to add some context on the use case for reordering this long list of items as some might wonder what this is for. So this is use for a questionnaire that has a long list of questions. Drag and drop might not best suited for the persona of the users thus, I'm exploring some options and alternatives. Thanks to everyone who have shared their solutions and suggestions.