I wasn't always like this with SAs. Like you I was very polite and didn't want to interrupt them but then I had an epiphany. They are getting paid to serve me! Just like I was getting paid to give great customer service to EVERYONE when I was a SA in an upscale department store.
Firstly, its about attitude. If you intend to buy something, be confident. Usually, I greet the closest SA before they get a chance to greet me. That means I'm watching them, they have acknowledged me and I ready to rumble.
Big smile, but stern voice. Hello, please show me the XYZ behind you, please. If they give attitude, again, I will say something along the lines of "not having a good day?" That usually breaks the ice.
If I get an eye roll or they sigh etc, again.. I acknowledge that and say something such as "If you're busy with another customer, please find me another SA, if not, show the XYZ."
Again - there's no grovelling. Remember, they don't own the merchandise. Rarely these days do the owners of stores, especially large ones, are the SAs. They don't own Chanel, or Celine or LV or
Coach or even your local thrift shop. Remember that. It's you and your $ keeping them in a job.
There have been times when there are SAs on the phone to their boyfriend or making plans for their night out. I interrupt them. YES. I don't wait for them to finish their conversation. OTOH, if I hear them talking on the phone to a customer or another store - you can usually tell because they will be using sku's and codes etc, I wait.
If you were closer, I would take you shopping with me! There are so many subtlties and nuances to use in your voice and actions.
I know one thing that irks the SAs is when customers mishandle or mistreat merchandise. I had an experience in Chanel a couple of years ago. It was the boxing day sale. I was still looking around, it was busy but I made sure I spoke to a couple of SA's as I wondered around. A simple "Hello, busy day ahead for you". Anyway. I went up to have a look at some CJ. There was a lady standing next to me with her friend/sister. The SA was wearing a glove to show her a beautiful suede like jumbo. This customer, instead of being a gentle with it, grabbed it round the bottom and squashed it. I was so horrified I said to her in a loud voice "WHAT ARE YOU DOING??"
I could see the SA was horrified at what the customer was doing but could not say what I did. The SA mouthed a relieved "thank you". I tell you what, I received not great but AWESOME service, even putting aside sale items for me for a couple of days till I made up my mind or when I came in next. Drinks, private room, friendly chat etc.
Hope this all helps. Remember, it'your money and your time. They are there to serve you but you are not their master. A little respect and acknowledgement goes along way.