PowerPoint Tip: Reformatting a presentation
The first thing I suggest you do is check the Slide Layout of the existing slides. This is the one area that causes more problems than almost any other area. Unfortunately, most presenters don't know that they should select the appropriate layout when they create a slide. They just use the default bullet point layout and delete or move items until they get the slide they want. The problem is that once you apply a new design to a slide, it wants to use the underlying layout and it moves things back to where they are supposed to be. So, before you reformat or insert any slides, review the layouts and apply or reapply the correct layout to each slide. You may also need to move text from randomly placed textboxes into the correct placeholders so it will format properly when inserted into a new design.
The second area you need to check before merging or reformatting is the new Slide Master. Too often Slide Masters are poorly constructed. Look for and fix the following: background graphics should be on the Slide Master and not on each individual slide; title and body text placeholders should have the correct font, size, alignment and color set on the Slide Master and not individually on each slide; and footers and slide number placeholders should be properly formatted and set to display if desired. By fixing the Slide Master before inserting any slides, you will save yourself a lot of time.
Finally, you are ready to assemble the new presentation. I suggest you open a new presentation and apply the design from the Slide Master you fixed in the previous step. Next, open the existing presentation and copy the slides into the newly formatted presentation, allowing the new design to be applied automatically. This will correct most problems, but some will still exist (it seems to be inconsistent sometimes). So the final step is to check each slide and reapply the layout if needed. You may also need to make some final fixes to the position of elements due to background graphics that may be in a different position in the new design.
Initially, it sounds like the pre-work will take some time, and indeed it will. But my experience is that it takes much more time to correct all the problems manually if you don't set yourself up by fixing the source files first. Try it out the next time you have to merge slides or apply a new design and let me know how it works for you.