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There could be several reasons your connection is slower.First your rural loop(line) is
probably copper ,Has load coils & may be range extenders for voice quality.Voice quality is what the telephone company is concerned with.You mentioned the minimum requirements for the phone company .They are so low they are useless.Last time I checked something like 14k.
Not much you can do about any of that.Here are some things you can try.
1.Disconnect eveything plugged into a phone jack in your home but your computer modem.Especially any phone you have connected to the modem(something you should never do even if it has a socket ).Then test your connection speed.If it improves
then one of the phones or other items plugged in the home telephone wiring is slowing the speed.Plug them back in one at a time till you find the problem one.
2.Replace the telephone wiring in the home if it is old.Use good quality telephone cable.(Not Walmart cheap) .Do this from the NID box in the whole house.Such as cat3 no smaller than 22 gauge sheilded.
3.Replace the modem.I get better results with an internal modem in a PCI slot.I tried an external serial modem & it was consistently slower.You will get advice in the opposite direction on this but this is what I found.
Read some of the topics in the dial-up section here & see if any of the tweaks help.
Like putting 115200 as maximum speed instead of 57600.
I won't suggest any modem strings because you need to put them in for your specific modem.They are simular but not exactly the same .These are the ones I use:
S91=15;S10=60;S25=100
S91 is for transmit dBm level for my modem 15 is the dBm level.
S10 Lost carrier hang up delay
Set the length of time the modem waits before hanging up after a carrier loss.
Range: 1 - 255 tenths of a second
 60 is the the delay I use so may modem tries to hold the carrier for 10 seconds before hanging up.This helps with disconnects.
S25 Delay to DTR
Set the length of time the modem ignores DTR before hanging up
Range: 0 - 255 hundredths of a second.This also helps delay disconnects.
In the registry I changed this.
W3 or W2 in some modems makes the modem report DCE speed instead of DTE
speed.
As I said these are modem specific yours may be the same or not.So just make sure before you try them.
This is from my dial-up connection:

let me see if i can hook up my dialup moden =)

Have you checked to see if there are any local wireless providers around?? (ie: Wi-Fi)

Another possible option.

edit: Welcome to the forum; I missed the 1st post thingy.

The top speed i have ever gotten when i had dial-up was like 42Kbs or something. Its to bad your not avaliable for cable or dsl though! I know how much of a pain dial-up is, never want to go back either  If your desperate you can pay anhwere from $60-$100 a month for satelite internet

You said you are in a rural area and others around you have the same problem. This leads me to believe that the houses in the area are slightly old? If so you may be suffering because of the phone-line. It is possible that it is not modern day's Touch-Tone, and may be Pulse. To decipher this, when you dial out do you have a pause between each number filled with a sound? Instead of Touch-Tone which is beep beep beep, Pulse is beep....beep....beep, kind of a dull ticking sound if you will.   

I use to get slow speeds like that also, then i called Embarq and got a new phone line put into the house and now i connect at 50Kbps all the time now.

::::::::::.. testmy.net test results ..::::::::::
Download Connection is:: 70 Kbps about 0.07 Mbps (tested with 97 kB)
Download Speed is:: 9 kB/s
Upload Connection is:: 26 Kbps about 0 Mbps (tested with 97 kB)
Upload Speed is:: 3 kB/s
Tested From:: http://testmy.net (Server 1)
Test Time:: 2007/07/13 - 8:25am
D-Validation Link:: http://testmy.net/stats/id-1PM8BYEWJ
U-Validation Link:: http://testmy.net/stats/id-BYZ9LWGE7
User Agent:: Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.2; .NET CLR 1.1.4322)

Just did that speed test so not that bad at all.

so then it is most likely your phoneline, so i'd check into getting updated to the Touch-Tone system.