For my own satisfaction, I generated just over 10GB of data spread across 4 files:

23/09/2016  20:18     2,737,000,000 data1.txt
23/09/2016  20:18     2,737,000,000 data2.txt
23/09/2016  20:18     2,737,000,000 data3.txt
23/09/2016  20:18     2,737,000,000 data4.txt
               4 File(s) 10,948,000,000 bytes
[download]

That vaguely approximated your described data:

C:\test\10gb>head data1.txt
@NS500278
GCGCCGGCGGCCATAGGGGCTGGTCAGTAAGAAGTAATGTCCCCAGCTGATTCGGATGGTGCGAATAAGG
+TCTTATCACTTACCCAAAGTATCTGGCTCTATATTGAGATACCGGAAGCCCCTTGTTGGTACTATGTGA
+TCGATATTTCT
+
=G=C=TATAAA=TGGTTG==C=TAT=GT=C==TAA==CCTA=AAACTTAAG==T=TTTGTCCAGGTAGCG
+TC=CCA=TG=TA=CT=TT=CC=AA==TCA=ACCGTCGTGGCC=A==GAA=AT=TCAGGCC=CC=GCTAG
+TG=CCA===TA 1

@NS500278
GTATACCGGTTGAAACAACACGAGAACGAAAGGGTCGCGACTCCATCATAAGGCTAGAAAACCAATTGTA
+TGGATCTGAACATGTTGTGGCGTTACGCGGAACTCCCTGGCTAAAGTGAGACGATTATCAATAGAAAGC
+AAACTCTACGT
+
AAAC=A=CTC=ATCAA==TGATACCGACCT=CCG=CCAG=CC=G=TC=TGGTG=GAGGTAGGT=AAC=GC
+ACA=CC==GTGGACCCTA=C=C=CG==TA=G=CCA=G==CTGGCGTT=CCGAACAGGC===ATCGATC=
+=TTTCTTTTTT 2
[download]

I implemented the code I described under How would I attempt the task as now described? in 55 lines, and ran it:

C:\test\10gb>..\1172352 *.txt > combined.out
Pass one found 1048269 groups of records in 4 files in 361.736613 seco
+nds

Total time:4826.534832 seconds
[download]

So 1 hour 20 minutes. My "couple of hours" gestimate wasn't too far wrong.