Put ID at beginning of data lines

I never quite got a good handle on the use of hold space, so I need help with taking a file which has identifying information for a person on one line, followed by data points on lines starting with a blank space for each data point.  There could be anywhere from 1 to dozens of data  lines per individual in the file.

I am running GNU sed version 3.02 on Linux.

Here is a sample input file:

"1","V3","Johnny Jamison"
 144058604,149864828
 104132262,115218852
 40739561,80546082
"2","V2","Janet Anne Doe"
 145956371,150258170
 125505743,131005138
 53487753,77418759
 32142804,34367848
"3","V2","William Jones"
 121742874,124782881
 89861384,107281037

Note that some people may have identical ID information in the first field, so ^" is what I am using to indicate that the line is the one with ID informtion on it.
 
The output I would like to generate from the above input data would look like the following:

"1","V3","Johnny Jamison",144058604,149864828
"1","V3","Johnny Jamison",104132262,115218852
"1","V3","Johnny Jamison",40739561,80546082
"2","V2","Janet Anne Doe",145956371,150258170
"2","V2","Janet Anne Doe",125505743,131005138
"2","V2","Janet Anne Doe",53487753,77418759
"2","V2","Janet Anne Doe",32142804,34367848
"3","V2","William Jones",121742874,124782881
"3","V2","William Jones",89861384,107281037  

It took quite a bit of work to take the original single line format for the data for each person, and turn it into the input format I am showing you above.  But now that I have massaged the data into something I think should easier to work with, I am stumped.

If I try the standard code for joining lines, I get the data all merged back together again:

$ sed  -e :a -e '$!N;s/\n /,/;ta' -e  'P;D'  testx.txt
"1","V3","Johnny Jamison",144058604,149864828,104132262,115218852,40739561,80546082
"2","V2","Janet Anne Doe",145956371,150258170,125505743,131005138,53487753,77418759,32142804,34367848
"3","V2","William Jones",121742874,124782881,89861384,107281037 
$

Putting code into a sed script, I tried:

$ cat x.sed 
/^"/,/^ /{
h
G 
s/^\(".*"\)\n /\1,/
} 

And I got duplicate lines and no prepending of ID information:

$ sed  -f x.sed  testx.txt
1","V3","Johnny Jamison"
"1","V3","Johnny Jamison"
 144058604,149864828
 144058604,149864828
 104132262,115218852
 40739561,80546082
"2","V2","Janet Anne Doe"
"2","V2","Janet Anne Doe"
 145956371,150258170
 145956371,150258170
 125505743,131005138
 53487753,77418759
 32142804,34367848
"3","V2","William Jones"
"3","V2","William Jones"
 121742874,124782881
 121742874,124782881
 89861384,107281037
$ 

I have tried a number of other ways, with varied (and often much uglier) results, none getting any closer to the desired  output.

I think I do prefer using a sed script for this than trying to make a one liner.

Suggestions?

Thanks,
Eliana