Stumbling

I'd say they could all be correct if used in the proper manner.

I stumbled upon a new book at the library.

I stumbled across the cost section in my presentation to the council.

I stumbled on a loose floorboard.

I stumbled into the room.

I stumbled in the bathroom.

I stumbled onto the grass.

The sentence I was wondering about is

" I just stumbled in the Guardian Weblog's Report."

According to your list I should have used stumbled upon, if I am not mistaken.

Things can get funny when people talk about web pages. To me, several of them could work.

I just stumbled upon the Guardian Weblog's Report.

I just stumbled across the Guardian Weblog's Report.

I just stumbled into the Guardian Weblog's Report.

I would probably use:

I just stumbled onto the Guardian Weblog's Report.

I am sorry to report that native English speakers do not differentiate their prepositions well. Many of these options are used interchangeably. This is because "stumbled on" is an idiom for finding something by accident. A few would be considered wrong.

I stumbled upon - I found by accident (only)

I stumbled across - I found by accident (or) I tripped when walking over

I stumbled on - I tripped when walking over. (Also, "on" is commonly used interchangably with "upon", though this is not technically correct.)

I stumbled into - I tripped while entering (or) I tripped and fell against

I stumbled in - I tripped while I was located in (only)

I stumbled onto - I tripped and walked on (Also, "onto" might be used interchangably with "upon", though this is not technically correct.)

I stumbled over - I was tripped by OR (less frequently) I found by accident

I stumbled upon and I stumbled on can be used for the same thing. I stumbled on a new piece of information/I stumbled upon a new piece of information. Into could be also used this way. Stumbling upon or on seem to imply that whatever you stumble upon is hidden and not clearly visible. Stumble into implies that what you are stumbling into is visible but not noticed all the time.
Across as I stumbled across a piece of information seems to be used for things you had originally, had put away or forgotten and then as you are researching something else you stumble across this other information.

I stumbled upon the answer.

Stumbled across the bedroom.

Stumbled on (probably not)
Stumbled into Jane.
Stumbled in the door? Maybe, not often.
Stumbled onto (not often)

Why not...web search results:

stumbled upon: 1,500,000
stumbled across: 1,410,000
stumbled on: 705,000
stumbled into: 561,000
stumbled in: 163,000
stumbled onto: 417,000

None of these phrases are idiomatic; they are all normal uses of prepositions.