Cross tolerance will manifest no matter what when a person switches from one opioid to another, but the degree to which this physiologically presents is variable due to a number of factors. Metabolism will play a big role- for example, someone who is a poor metabolizer of codeine due to a[n] enzyme (CYP2D6- or 3A4??) deficiency may require larger doses to achieve the desired effect, yet if that same person takes an equipotent dose of morphine, the effects would be much more pronounced. Therefore a lesser dose is necessary for the needed result, regardless of tolerance.
Speaking in very general terms, as to the extent of cross tolerance between natural opiates and semi-synthetics: Based on what I've learned through research and experience it's not a simple 1:1, meaning a dose of say morphine is not likely to translate exactly to an equivalent dose of hydrocodone. But regardless of whether or not an opioid is natural, semi-synthetic, or synthetic, a cross tolerance will exist, and no two opioids are exempt from this phenomenon; there is no combination that allows a person to develop a tolerance to opioid X and then simply switch to opioid Y and start over, as it were. Aside from metabolism, the pharmacodynamics and pharmacokinetics, or the known properties of the drug and how they interact with the body and CNS, will play a significant role in determining the degree to which two opioids compare on a dose-response curve. Also, the length of time in which one opioid was taken, how the transition to the other opioid was carried out, other drugs' potential interactions, diet, lifestyle, and so forth will contribute as well. Plus, it's important to remember that the perceived effects of one opioid in comparison to another, or really of any two drugs in the same class are highly subjective, and difficult to accurately record or express definitively in a qualitative manner.
With that said, this is a complicated subject with piles of contradictory information, and no shortage of differing opinions which are often based on anecdotal evidence, which is itself often based off of personal experience (especially in a forum like this). Personally, I'd guess that the analgesic strength of oxycodone/acetaminophen is going to be greater than that of kratom, PPT, or codeine even when taken at lower doses. And the fact that you got this from a hospital, a prescription medication intended for relieving pain, probably led to an expectation (whether consciously or not) that it would do what it's supposed to do, and so it did.
As for laxatives, in my experience the best quick fix is magnesium citrate. It's a non-viscous liquid that is very cheap and will clear you out almost guaranteed. One 12oz or so bottle is usually a dollar or less, and depending on the severity, that amount should be adequate for at least one or two doses. Honestly, take caution because one time I was seriously backed up and drank the whole bottle, and the next day I must have shat a dozen times, essentially going from constipation to diarrhea overnight. Also, a good preventative motility "helper" is ducolase sodium. If you intend on being slow due to opiates, this is a good supplement to help move things along but not cause the undesirable side effects associated with stimulant laxatives.
