Can't Swallow A Tylenol, So How Can I Swallow The Iodine Pill?

So, I had a total thyroidectomy in June due to papillary thyroid cancer.  Today, I'm going for my first thyrogen injection.  On Wednesday, I am going for my RAI.  I am not scared of getting the injections.  I can handle that, although I hate needles.  However, I have issues with acid reflux, and it has gotten worse over the past few weeks.  On and off I have issues with the feeling of a lump in my throat, and feeling whatever I swallow come back up.  I've had this before, but it has been a long time since the reflux has been acting up like this.  I don't know if this is a side effect of my Synthroid (which was just reduced from 125 to 112 mcg this week), the low iodine diet, or who knows what.  So, the dilemma at hand is that I have issues swallowing pills due to my reflux.  I have to chew Tylenols, haven't even tried to swallow a whole one in years because I can't get it past my mouth.  Even swallowing my protonix and synthroid, which are both small, is a chore.  I don't chew them, but I have to hold my breath to force myself to eventually swallow them.  Even then, it can take several minutes (no, I don't hold my breath the whole time, I eventually take a breath through my nose) of holding the pill in my mouth and bending forward to finally get the urge to swallow it down.  I brought this up to my doctor who informed me that if I could eat a cheeseburger, then I can swallow the pill, which they say is about the size of a Tylenol gel cap.  Hate to tell him this, but I can't eat a cheeseburger without chewing it into miniscule pieces, and even then it's hard to swallow.  They refuse to give me the liquid because it's too volatile and hazardous to staff.  I don't want to hurt anyone, but I'm scared of how big this pill might be and what might happen if I choke on it (which has happened before with other foods and pills).  I have no choice but to go where I'm going, there is nowhere else within a 2 hour drive to go for treatment, so I'm stuck.  The physicist at the doctor's office said he would order the smallest pill possible (I'm getting a dose of 50 millicuries), but I'm still concerned.  He also suggested that I try to take it with applesauce or pudding, which I may try, but being on a low iodine diet I can't have pudding to try this ahead of time.  If the pill is the size of my protonix (40 mg, I think), I think I can manage this.  However, any bigger than that and I'll be tempted to chew it up, which I'm told they frown upon, obviously.  Does anyone know how big this stupid pill might be? Also, any idea of the ramifications if I end up chewing this stupid pill? Maybe it's my meds being off that has me so fixated on this, but eating anything has been slightly harrowing ever since I started having dysphagia eight years ago.  Anyone got any suggestions as to how to swallow this stupid pill?