First do not pay for anything, it can all be done as well as anything commercial for free although it might be 10 seconds slower. Most of these techniques will force you to lose the menus as Sir-Fritz says, anything that requires encoding a stream is almost certain to.
First this appears to be a pure PAL-NSTC video thing rather than region coding, still such things can be broken (if necessary, many players are multi region and most DVDs like your example one come without region coding or even encryption). I assume you already have this down though. Personally I would lay some blame with the standalone player and while the following methods may be largely free it may be worth just finding one of those cheap Chinese players for in many ways they are probably better than the expensive stuff.
As for NTSC. Resolution issues aside (PAL is higher res than NTSC) the main problem would be framerate (PAL is 25 and NTSC is 30 or you can double those numbers for interlaced video (which DVDs use) by splitting the frame in two and calling it field rate).
Hardly anything is shot at 30fps (sports and news being the main two) so the vast majority of NTSC video uses a technique called pulldown, here various fields are played multiple times to get the apparent framerate up to speed. The most common is the 3:2 pulldown but as anyone who has done any video work will tell you it is not always the case (odd pulldown methods ranging from minor tweaks to insanely complex methods, mixture of pulldown and true NTSC (anime is a major culprit here as are most shows that make heavy use of CGI*). It is explained more here:
http://www.zerocut.com/tech/pulldown.html
and here:
http://atv.hamradio.si/V-INT.HTM
Note that is for FILM video (24 fps) not PAL (25 fps although PAL is often sped up FILM as most people can not tell the difference even with a side by side compare, NTSC viewers are more likely to see it and vice versa PAL viewers are more likely to see the "jerky" nature of NTSC).
*this is the "percentage film" thing that DGMPEGdec gives you.
Methods:
duping the player: your DVD player of choice is able to "play" the video but it does not like the fact it is in "PAL" format when it initially tries to decode things. You make it think it is NTSC by using vobblanker or ifoedit and then it is a matter of hoping that the player works.
Vobblanker
http://www.afterdawn.com/software/video_so.../vobblanker.cfm
ifoedit:
http://www.afterdawn.com/software/video_so...ols/ifoedit.cfm
You could probably also do it with PCGedit but even having used it for years now I am still scared by it.
You need to decrypt the DVD and load it up in one of those apps (you want the VIDEO_TS.IFO on both counts rather than any of the later files). Double click the sections that say PAL in ifo edit or right click and select "video attrib" in vobblanker.
Remember this is a kludge of the highest order, it may not work at all and even if the end result does play you are not assured of anything. Being the simplest method and with writable DVDs costing less than a chocolate bar I would consider this first.
hard telecine:
Here the pulldown occurs and each "new" field is saved as part of the video stream rather than being a virtual field as it were. I do not suggest doing this and indeed I spend most of my time when ripping various DVDs trying to get just this sorted (it seems more than a few DVD production houses do no have a clue). Not to mention it is a horrific waste of space and that combined with MPEG2 encoding does not make for good video.
pulldown flags:
Here the video stream/container is parsed and the player/decoder then inserts fields as required, this is the usual way DVDs work.
This app is good for PAL to NTSC and just about every other conversion out there or that you can think up but before that you will need to get the video in the correct format.
http://neuron2.net/dgpulldown/dgpulldown.html
Apps for the job
You will need to demux the video first.
http://neuron2.net/dgmpgdec/dgmpgdec.html
http://www.videohelp.com/tools/ReJig also works
Deinterlacing may be a problem, you can try doing it but you may end up with fields of out order (likely very jerky playback) and a whole mess of a video.
Basics:
http://www.100fps.com/
Methods, covered above but AVIsynth and some of the newer stuff is likely to be better.
http://neuron2.net/mine.html#avisynth has some good stuff.
Resize can be done in AVIsynth or possibly at the encoder level, I would suggest doing it as making a file not compliant with the DVD spec is not such a good idea (especially if the current player can not even play back PAL). It might be worth mentioning that some DVD makers, especially in PAL regions, do very odd things with video size and aspect ratio (usually for legit reasons but it can still be a pain to work with).
Encoding, several apps here
HCenc and QuEnc being the main two, here is HCenc
http://www.bitburners.com/hc-encoder/ quenc is on the same site. HCEnc is my choice of app and it nicely has the ability to check you are doing DVDs properly.
The encoders will make an elementary stream (a .m2v file) which you can serve up to DGPulldown.
From here you need to mux the stream into DVD format, there are countless apps for this and I use loads of them.
rejig, muxman, ifoedit, quenc, dvdstyler and much more.
http://www.dvdstyler.de/index.php?option=c...=53&lang=en
Most of them will want you to forgo menus or make your own. If you want to keep them and are up for a challenge then:
http://forum.videohelp.com/topic313743.html
A note on audio, PAL DVD allows for MP2 audio and while it is not used all that often it is not part of NTSC players and will usually not work with them. Your DVD is somewhat offbeat though and in my experience those are the ones most likely to use it, if it is the case you will need to convert the audio to AC3 (I do not suggest using DTS for anything).
And finally all in one apps. As you have probably just seen video is a complex thing which is not helped by standards people taking the lazy/cheap/uncompetitive route and automated tools can never really do it justice until someone decides to make a good AI so I do not really like them. Most of them use older versions of the software I just mentioned or cheap and nasty implementations of simple methods too.