Okay, I'm going to try out my system using a 25 point baseline and no fudging. I realized that I had to add two clarifications to get the system working:
1. When calculating point total, any score of 8 or lower is worth 0 points.
2. Raising any score from 3 to 7 is done on a point for point basis.
ATTEMPT 1 - THE FIGHTER
Roll 1: 1, 1, 4 = 6 = Str
Roll 2: 2, 1, 6 = 9 = Dex
Roll 3: 4, 1, 1 = 6 = Con
Roll 4: 5, 6, 2 = 13 = Int
Roll 5: 6, 6, 6 = 18 = Wis
Roll 6: 2, 1, 6 = 9 = Cha
I'll swap wisdom and strength. Total point value is 22, 3 below baseline. This means I get 4 points to spend. I'm putting them all into con, giving me:
Str: 18
Dex: 9
Con: 10
Int: 13
Wis: 6
Cha: 9
I qualify for expertise and have a devastating strength but suffer from some drawbacks as a result of natural shortcomings. The low wisdom is quirky and could be fun.
ATTEMPT 2 - THE WIZARD
Roll 1: 1, 5, 5 = 11 = str
Roll 2: 4, 2, 4 = 10 = dex
Roll 3: 3, 3, 3 = 9 = con
Roll 4: 5, 3, 5 = 13 = int
Roll 5: 1, 2, 6 = 9 = wis
Roll 6: 5, 4, 5 = 14 = cha
I'll swap charisma and constitution. Total point value is 18. This gives me 7 extra points to spend. I'll bump int to 16, costing 5 points, then dex to 12, costing 2 more.
str: 11
dex: 12
con: 14
int: 16
wis: 9
cha: 9
Nice - pretty close to what you'd get with standard point spread but a little bit tweaked to account for natural ability.
ATTEMPT 3 - THE ROGUE
Roll 1: 4, 4, 3 = 11 = str
Roll 2: 6, 1, 5 = 12 = dex
Roll 3: 2, 5, 6 = 13 = con
Roll 4: 1, 6, 2 = 9 = int
Roll 5: 3, 1, 3 = 7 = wis
Roll 6: 5, 4, 6 = 15 = cha
I'll swap dex and cha. Total point value is 21. I get four more points to spend. I'll bump dex to 16, and raise int and wis both by 1.
str: 11
dex: 16
con: 13
int: 10
wis: 8
cha: 12
Nice - very workable. It's close to standard point spread but the abilities aren't quite where a rogue would most likely place them.
ATTEMPT 4 - THE CLERIC
Roll 1: 5, 5, 4 = 14 = str
Roll 2: 3, 3, 1 = 7 = dex
Roll 3: 1, 6, 1 = 8 = con
Roll 4: 2, 1, 1 = 4 = int
Roll 5: 3, 4, 1 = 8 = wis
Roll 6: 3, 6, 6 = 15 = cha
I'll swap cha and wis. Total point value is 14 so I get 11 points to spend. I'll raise wis by 1 (to 16), int to 8, con to 10, dex to 8, and cha to 10.
str: 14
dex: 8
con: 10
int: 8
wis: 16
cha: 10
Definitely workable but a bit quirky, which is fun. Getting out of the "4 int pit" hurt some but the character is still workable.
ATTEMPT 5 - THE MONK
Roll 1: 5, 4, 4 = 13 = str
Roll 2: 4, 1, 4 = 9 = dex
Roll 3: 2, 3, 4 = 9 = con
Roll 4: 4, 3, 4 = 11 = int
Roll 5: 5, 3, 6 = 14 = wis
Roll 6: 3, 2, 4 = 9 = cha
I'll swap int and dex. Total point value is 17, giving me 8 points to distribute. I'll raise wisdom to 16, dex to 14, and con to 10.
str: 13
dex: 14
con: 10
int: 9
wis: 16
cha: 9
Looks almost like yer standard monk.
SUMMARY
From this limited test sample the results seem very similar to standard point buy, but eliminate the problem with characters choosing the same point spread for the same character classes. In addition, they provide the off chance of creating a very quirky character, like the fighter example, or a very exceptional character through extreme luck (considering you roll straight 3d6 not 4d6 drop lowest) of the dice, which did not chance to happen with my test cases but would no doubt eventually occur on a rather rare basis. All of the characters are quite viable.
I starting to like this system and I think I'm going to use it from now on. Maybe I'll run some more test cases. For anyone else that wants to, there is an online die roller here that helps generate the initial stat rolls quickly - just make sure to modify the settings because the web site defaults to 4d6 drop lowest:
http://www.irony.com/igroll.html