I feel like johnm should chime in here. I have a nice video of him doing arachnids with Don Olney's raffle top.
I called what I did for Mike 'Arachnids' but now I'll retract that to say I do something 'Arachnid-like', since I really don't understand the naming conventions for this type of action.
The action to which I'm referring is the feeding and retraction of string with the non-button hand to move the top up with retraction and lower the top with feeding. I've had runs over 60 with a fixed tip after boomerang and button hand drop (like merry-go-round) so the first 5-7 reps are really just slowing the top down to maintenance speeds. During the upper (top at the vertically high portion above the button hand) part of the trick, the top tip is towards me and the action after reaching the high position reminds me of the drop from the button hand when doing roller coasters . In particular, the top needs to ride down the string in good contact with the string under the influence of gravity since this is the regeneration portion of the motion for this version. During roller coasters, the non-button hand slowly feeds string by allowing the string to slip between the fingers and later in that trick the string is released and recaught near the button hand to again have a supply of string to feed out. In this Arachnid-like trick, the string feeding is accomplished by maintaining a constant grip on the string and increasing the functioning length by moving the non-button hand closer to the button hand, and by moving the non-button hand away, the top rises and a new supply of string is available to feed out.
The key to the trick seems to be controlling the feeding of string as the top is falling. Too fast and no regeneration free fall occurs coupled with a hard to control whip-catch like impact of the top back on the string. Too slow and not enough string is fed out before the top's precession requires you to pull up which results in various problems like a hand crash or panic launch. Speaking of the precession, the top begins to rotate when the string tension resumes after passing above the button hand and continues until the tension is released sometime during the upstroke thus resulting in a twist of the string which is removed by passing the top over the button hand. One training trick is to allow one twist to form and remain in the string before beginning the repeated cycle. I've found the single twist still allows the string to slide past itself reasonably well while providing an extra bind on the tip which helps to keep the top on the string. I usually loose the top by it gently slipping out of the string just at the beginning of the fall after passing over the button hand. The single twist and resulting bind does slow the top significantly but 20 or so reps are possible which is enough to practice the motions. In addition to all this up-down stuff you have to worry about side to side action with the button hand to maintain the top at a reasonable angle to keep it on the string--slightly point down but mostly horizontal seems best for me.
But the top takes at least the same amount of time going up
Intuitively, it seems to me that there is more regeneration potential on the reverse bind, as you cannot eliminate the friction on the way up but you could decrease it in theory on the way down by feeding string fast enough.
The time going up depends on how quickly you pull while the drop relies on gravity and your feed rate. What is roughly the same for up and down should be the length of string passing the tip. The way up sometimes resembles the 'pop' at the bottom of a roller coaster if you both pull the string with the non-button hand and lift up with the button hand so the top doesn't experience any string drag on the way up. Whether this is a proper motion or not is something else