I agree that learning to read either tab or traditional notation is essential for training the brain and fingers together.
Do you have a book like "Building Walking Bass Lines" by Ed Friedland? It doesn't have to be that one, but it comes with a DVD and the song is played for you on jazz piano - you play along with simple bass lines.
I didn't get a chance to look at the songs you're trying to play, but you probably need to choose very slow tempo songs at first - or as RedSubway said, very simple lines (or both).
Do start playing songs, even if out of tempo and too slow at first. It's great if you can find people to play with you, too - really helps.
You can play a song like Autumn Leaves by just hitting one note (a whole note - 4 beats) per bar, and it will sound cool if played with a keyboardist or guitarist. That gives you real practice in seeing whether you really know those notes on the fretboard. It goes like this (in its simplest form):
A-D-G-C
F#-B-E-E
A-D-G-C-
F#-B-E-E
B-B-E-E
A-D-G-C
F#-B-E-E
F#-B-E
Notice that this also introduces you to the structure of one common type of simple song. Songs usually have repeat elements, so once you've broken it down into phrases, and you learn one phrase at a time, you build it back up again. Playing an entire song before you're ready with the skills is very very tough. If you were in a practicing band, where everyone played at about your level, that's what you'd be doing: breaking it down into 2 and 4 bar and then 8 bar phrases.
You can do this with half notes next, then quarter notes (I'd transcribe it all into standard notation, if I were you - because reading rhythm and notes together may be the essential skill you need to pick up next, for songs).
This can be practiced, obviously, with a metronome. I'd be very surprised if you weren't playing the whole song by the end of today. It really does sound like a song, even if no one is playing with you, and even if you don't know the tune.
Hopefully, you know the tune.
You need to stretch your memory skills to encompass all the changes that come with a typical song, and then get your fingers up to speed.
Do you have the chords to the two songs you're trying to play? If so, start with the same method (just playing two half notes or 4 quarter notes, if it's in 4/4- not a rhythmic line) until you get the structure, then stick the rhythmic line in.
If you're a beginniner and you're choosing songs that have repeated changes in time structure, you're just making it too hard for yourself.