Why is the toilet not flushing completely

I have reviewed the other questions here related to this. I'm pretty sure it's not clogged because it doesn't back up and usually only takes 2 flushes to get everything down. Usually it seems to be paper that's left after the first flush, which seems odd. The water does swirl, but it does seem to be kind of a weak swirl, for lack of a better term. The water and paper just doesn't go all the way down.

Here's what I've tried already:

• used a plunger
• used a snake/auger, going down from the toilet
• used a snake/auger, from the roof, going down the vent; it was maybe 15 feet long; it came back wet but clean
• held down the handle to make sure the entire contents of the tank is emptied; this didn't have any effect, it still didn't flush completely; although I did notice that when I didn't hold it down, it did seem like the flapper closed early, so I should probably try a new flapper
• took out the 'filler' in the tank; there is a large plastic spacer thing in the tank which I assume is there to take up volume and save water; I removed this so that the tank was completely full; still no change
• we have hard water, but we've had a water softener for the last 12 or so years we'e been in the house (out of 15); so I'd think any mineral deposits wouldn't be there, or at least wouldn't suddenly appear; I haven't done the CLR scrum around the rim jets yet
• I tried pouring in a couple gallons of water from a bucket to see if it goes down, which it started to and then stopped; I don't know what this may indicate

This is in an upstairs bathroom. I don't hear any gurgling out of the sink or bath when I flush.

This is the original toilet, or at least since we moved in 15 years ago; the house was built around 1988. I have replaced the flush valve or whatever you call the main mechanism inside the tank a few or several years ago.

It has been doing this for a few months now (yea I'm slow getting to it); I mean it's basically functional with a 2nd flush, just kind of gross.

EDIT: I finally pulled the toilet, after trying everything else (except CLR); I tried to snake/auger it from the bottom and didn't find anything there either; I couldn't get the snake all the way thru, but I feel like this is more due to the sharp bend; it just completely stopped; everyone will probably say this obviously means you have a clog, but it felt like it just wasn't turning, rather than hitting any obstruction. It's an older auger from my father; kind of spools out of a funnel shaped metal container, rather than the closet augers I've seen in related youtube videos

So now what? Might be easier at this point to just replace it, since I didn't change anything after pulling it, and I'm afraid if I put the old one back on I'll have the same probably since nothing changed