Aha - ProxyMethod should be ProxyType, and should be 1 not 3 for HTTP. I created a new session in PUTTY.EXE and saved it, then looked in the registry:
Windows Registry Editor Version 5.00
[HKEY_CURRENT_USER\Software\SimonTatham\PuTTY\Sessions\TEST]
"Present"=dword:00000001
"HostName"="TEST"
"LogFileName"="putty.log"
"LogType"=dword:00000000
"LogFileClash"=dword:ffffffff
"Protocol"="ssh"
"PortNumber"=dword:00000016
"CloseOnExit"=dword:00000001
"WarnOnClose"=dword:00000001
"PingInterval"=dword:00000000
"PingIntervalSecs"=dword:00000000
"TCPNoDelay"=dword:00000001
"TerminalType"="xterm"
"TerminalSpeed"="38400,38400"
"ProxyExcludeList"=""
"ProxyType"=dword:00000001
"ProxyHost"="TESTPROXY"
"ProxyPort"=dword:00000000
"ProxyUsername"="user"
"ProxyPassword"="pass"
"ProxyTelnetCommand"="connect %host %port\\n"
"ProxySOCKSVersion"=dword:00000005
"Environment"=""
"UserName"=""
"LocalUserName"=""
"NoPTY"=dword:00000000
"Compression"=dword:00000000
"AgentFwd"=dword:00000000
"ChangeUsername"=dword:00000000
"Cipher"="aes,blowfish,3des,WARN,des"
"AuthTIS"=dword:00000000
"AuthKI"=dword:00000001
"SshProt"=dword:00000001
"SSH2DES"=dword:00000000
"PublicKeyFile"=""
"RemoteCommand"=""
"RFCEnviron"=dword:00000000
"PassiveTelnet"=dword:00000000
"BackspaceIsDelete"=dword:00000001
"RXVTHomeEnd"=dword:00000000
"LinuxFunctionKeys"=dword:00000000
"NoApplicationKeys"=dword:00000000
"NoApplicationCursors"=dword:00000000
"NoMouseReporting"=dword:00000000
"NoRemoteResize"=dword:00000000
"NoAltScreen"=dword:00000000
"NoRemoteWinTitle"=dword:00000000
"NoDBackspace"=dword:00000000
"NoRemoteCharset"=dword:00000000
"ApplicationCursorKeys"=dword:00000000
"ApplicationKeypad"=dword:00000000
"NetHackKeypad"=dword:00000000
"AltF4"=dword:00000001
"AltSpace"=dword:00000000
"AltOnly"=dword:00000000
"ComposeKey"=dword:00000000
"CtrlAltKeys"=dword:00000001
"TelnetKey"=dword:00000000
"TelnetRet"=dword:00000001
"LocalEcho"=dword:00000002
"LocalEdit"=dword:00000002
"Answerback"="PuTTY"
"AlwaysOnTop"=dword:00000000
"FullScreenOnAltEnter"=dword:00000000
"HideMousePtr"=dword:00000000
"SunkenEdge"=dword:00000000
"WindowBorder"=dword:00000001
"CurType"=dword:00000000
"BlinkCur"=dword:00000000
"Beep"=dword:00000001
"BeepInd"=dword:00000000
"BellWaveFile"=""
"BellOverload"=dword:00000001
"BellOverloadN"=dword:00000005
"BellOverloadT"=dword:000007d0
"BellOverloadS"=dword:00001388
"ScrollbackLines"=dword:000000c8
"DECOriginMode"=dword:00000000
"AutoWrapMode"=dword:00000001
"LFImpliesCR"=dword:00000000
"WinNameAlways"=dword:00000000
"WinTitle"=""
"TermWidth"=dword:00000050
"TermHeight"=dword:00000018
"Font"="Courier New"
"FontIsBold"=dword:00000000
"FontCharSet"=dword:00000000
"FontHeight"=dword:0000000a
"FontVTMode"=dword:00000004
"TryPalette"=dword:00000000
"BoldAsColour"=dword:00000001
"Colour0"="187,187,187"
"Colour1"="255,255,255"
"Colour2"="0,0,0"
"Colour3"="85,85,85"
"Colour4"="0,0,0"
"Colour5"="0,255,0"
"Colour6"="0,0,0"
"Colour7"="85,85,85"
"Colour8"="187,0,0"
"Colour9"="255,85,85"
"Colour10"="0,187,0"
"Colour11"="85,255,85"
"Colour12"="187,187,0"
"Colour13"="255,255,85"
"Colour14"="0,0,187"
"Colour15"="85,85,255"
"Colour16"="187,0,187"
"Colour17"="255,85,255"
"Colour18"="0,187,187"
"Colour19"="85,255,255"
"Colour20"="187,187,187"
"Colour21"="255,255,255"
"RawCNP"=dword:00000000
"PasteRTF"=dword:00000000
"MouseIsXterm"=dword:00000000
"RectSelect"=dword:00000000
"MouseOverride"=dword:00000001
"Wordness0"="0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0"
"Wordness32"="0,1,2,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1"
"Wordness64"="1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,2"
"Wordness96"="1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1"
"Wordness128"="1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1"
"Wordness160"="1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1"
"Wordness192"="2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2"
"Wordness224"="2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2"
"LineCodePage"="ISO-8859-1:1998 (Latin-1, West Europe)"
"Printer"=""
"CapsLockCyr"=dword:00000000
"ScrollBar"=dword:00000001
"ScrollBarFullScreen"=dword:00000000
"ScrollOnKey"=dword:00000000
"ScrollOnDisp"=dword:00000001
"LockSize"=dword:00000000
"BCE"=dword:00000000
"BlinkText"=dword:00000000
"X11Forward"=dword:00000000
"X11Display"="localhost:0"
"LocalPortAcceptAll"=dword:00000000
"RemotePortAcceptAll"=dword:00000000
"PortForwardings"=""
"BugIgnore1"=dword:00000000
"BugPlainPW1"=dword:00000000
"BugRSA1"=dword:00000000
"BugHMAC2"=dword:00000000
"BugDeriveKey2"=dword:00000000
"BugRSAPad2"=dword:00000000
"BugDHGEx2"=dword:00000000