I have a Daiwa Legalis 1000 with a non-removable handle paddle that needs grease. It has too much room and makes small clicking noises and I can feel it like a small fish strike. Normally I add some grease under the paddle to help float it and smooth it out but this Legalis must be too cheap and doesn’t have a screw to remove the paddle. Any suggestions to help push/flow some grease down into it? 
 

viscous oil - bushing oil or Phil Tenacious.  

In my experience oil only lasts a short time. The grease is thick enough to float the paddle around the stem 

Greetings @wasabi_VA

 

I was going to second @bulldog1935 recyou'llommendation of a viscus oil as the easier preferred solution. However, it is possible to get grease in there but it will be messy and require additional effort. 

 

If you are using the larger tube of the super lube food grade grease, you could attempt to press the tube right up to the opening on the reel handle and forcefully inject the grease. You'll need to make a hard seal by pressing quite hard and holding it in place while you squeeze the grease. 

 

The super lube uses the same thread on the tube as many other common tubes like those with silicone RTV. Those come with a multi-size cut to fit nozzle that screws on the tube. Be cautious of how much squeezing force you apply as you can burst the tube and then there will be more of mess. 

 

The other option is use a little heat. What you show in the photo is a good start. You could add a bit more. Keep it in that vertical position while adding some gentle heat from a hair drier. This will help the grease to flow in. Rotating the handle helps work it in too. 

 

Of course here in AZ we simply set it outside and let the sun do it. It gets plenty warm fast so things work well with the sun and gravity. 

Just $ 0.02 put in for consideration. Good luck!

I use ReelX oil a few times a season. I think the grease could end up getting reel messy.

When grease gets pushed out of the way - it's out of the way.  

Viscous oil will continue to flow into the bushing/spindle joint.  

Is there a specific packaging or brand that I can buy somewhere common like Walmart or an auto parts store?

Bike shops carry Phil Wood Tenacious oil - I checked Amazon, and their price was double what it should be.  

Also at bike shop, any brand freehub oil will work.