SUCCESS!!!System now boots (and reboots!

) with the desired settings --- 1366 x 768 on the external monitor and 1024 x 600 on the netbook monitor -- and each are "extensions" of the other (not clones).
I did everything in xorg.conf, with some help from xrandr (just to see the position of LVDS1)
# File generated by XFdrake (rev 262502)
# **********************************************************************
# Refer to the xorg.conf man page for details about the format of
# this file.
# **********************************************************************
Section "ServerFlags"
Option "DontZap" "False" # disable <Ctrl><Alt><BS> (server abort)
AllowMouseOpenFail # allows the server to start up even if the mouse does not work
#DontZoom # disable <Ctrl><Alt><KP_+>/<KP_-> (resolution switching)
EndSection
Section "Module"
Load "v4l" # Video for Linux
EndSection
Section "Monitor"
Identifier "VGA1"
VendorName "Generic"
ModelName "Flat Panel 1024x600"
HorizSync 31.5-55.0
VertRefresh 40.0-70.0
Option "PreferredMode" "1366x768"
Option "LeftOf" "LVDS1"
# TV fullscreen mode or DVD fullscreen output.
# 768x576 @ 79 Hz, 50 kHz hsync
ModeLine "768x576" 50.00 768 832 846 1000 576 590 595 630
# 768x576 @ 100 Hz, 61.6 kHz hsync
ModeLine "768x576" 63.07 768 800 960 1024 576 578 590 616
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1368x768_120" 185.67 1368 1472 1624 1880 768 769 772 823 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1368x768_100" 151.73 1368 1464 1616 1864 768 769 772 814 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1368x768_85" 125.67 1368 1456 1600 1832 768 769 772 807 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1368x768_75" 110.19 1368 1456 1600 1832 768 769 772 802 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1368x768_60" 85.86 1368 1440 1584 1800 768 769 772 795 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1368x768_50" 69.92 1368 1424 1568 1768 768 769 772 791 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1360x765_120" 182.63 1360 1456 1608 1856 765 766 769 820 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1360x765_100" 149.22 1360 1456 1600 1840 765 766 769 811 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1360x765_85" 124.65 1360 1448 1592 1824 765 766 769 804 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1360x765_75" 108.34 1360 1440 1584 1808 765 766 769 799 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1360x765_60" 84.40 1360 1424 1568 1776 765 766 769 792 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1360x765_50" 69.34 1360 1416 1560 1760 765 766 769 788 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1280x720_120" 161.56 1280 1376 1512 1744 720 721 724 772 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1280x720_100" 131.85 1280 1368 1504 1728 720 721 724 763 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1280x720_85" 110.01 1280 1360 1496 1712 720 721 724 756 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1280x720_75" 95.65 1280 1352 1488 1696 720 721 724 752 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1280x720_60" 74.48 1280 1336 1472 1664 720 721 724 746 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1280x720_50" 60.47 1280 1328 1456 1632 720 721 724 741 -HSync +Vsync
EndSection
Section "Monitor"
Identifier "LVDS1"
VendorName "Generic"
ModelName "Flat Panel 1024x600"
HorizSync 31.5-55.0
VertRefresh 40.0-70.0
Option "PreferredMode" "1024x600"
Option "Position" "1366 0"
# TV fullscreen mode or DVD fullscreen output.
# 768x576 @ 79 Hz, 50 kHz hsync
ModeLine "768x576" 50.00 768 832 846 1000 576 590 595 630
# 768x576 @ 100 Hz, 61.6 kHz hsync
ModeLine "768x576" 63.07 768 800 960 1024 576 578 590 616
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1024x600_120" 107.41 1024 1096 1208 1392 600 601 604 643 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1024x600_100" 87.51 1024 1088 1200 1376 600 601 604 636 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1024x600_85" 72.83 1024 1080 1192 1360 600 601 604 630 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1024x600_75" 63.20 1024 1080 1184 1344 600 601 604 627 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1024x600_60" 48.96 1024 1064 1168 1312 600 601 604 622 -HSync +Vsync
# modeline generated by gtf(1) [handled by XFdrake]
ModeLine "1024x600_50" 39.55 1024 1048 1152 1280 600 601 604 618 -HSync +Vsync
EndSection
Section "Device"
Identifier "device1"
VendorName "Intel Corporation"
BoardName "Intel 810 and later"
Driver "intel"
Option "DPMS"
Option "MonitorLayout" "NONE,CRT+LFP"
Option "monitor-VGA" "VGA1"
Option "monitor-LVDS" "LVDS1"
EndSection
Section "Screen"
Identifier "default screen"
Device "device1"
Monitor "LVDS1"
DefaultColorDepth 24
Subsection "Display"
Depth 8
Modes "1366x768" "1360x765" "1280x720"
EndSubsection
Subsection "Display"
Depth 15
Modes "1366x768" "1360x765" "1280x720"
EndSubsection
Subsection "Display"
Depth 16
Modes "1366x768" "1360x765" "1280x720"
EndSubsection
Subsection "Display"
Depth 24
Modes "1366x768" "1360x765" "1280x720"
EndSubsection
Subsection "Display"
Depth 8
Modes "1024x600"
EndSubsection
Subsection "Display"
Depth 15
Modes "1024x600"
EndSubsection
Subsection "Display"
Depth 16
Modes "1024x600"
EndSubsection
Subsection "Display"
Depth 24
Modes "1024x600"
EndSubsection
EndSection
Section "ServerLayout"
Identifier "layout1"
Screen "default screen"
EndSection
Many thanks to you, AS, and the whole PCLinuxOS community.
