It seems to me that you are not the first person who ask the same question. Recently I asked on the close question (read many comments to the answer). Another old answer including the demo could probably answer on some your opened questions.

Your code using beforeRequest don't work just because the function beforeRequest will be caled immediately before the ajax call and the changing of the search parameter is too late. Moreover overwiting of filters everytime is probably not the best idea. In the case the user will not able to set any other grid filter.

So I can repeat, that the imlementation of the solution which you need is very simple. You should just set filters property of the postData parameter of jqGrid to the filter which you need and set another jqGrid parameter search:true additionally. It's all! Later the user will be able to open advance searching dialog and overwrite the filters. The user can also click on Reset button of the advance searching dialog and set filters to empty string and search:false.

For better understanding I have to clear how search parameter or some other jqGrid will be used in the URL. There are parameter prmNames of jqGrid which defines the names of parameters send as a part of URL or as a part of data POSTed to the server. The default value of prmNames contain search:_search and the code of internal populate function used by jqGrid has the following simplified code fragment:

var prm = {}, pN=ts.p.prmNames;

if(pN.search !== null) {prm[pN.search] = ts.p.search;}

if(pN.nd !== null) {prm[pN.nd] = new Date().getTime();}

if(pN.rows !== null) {prm[pN.rows]= ts.p.rowNum;}

if(pN.page !== null) {prm[pN.page]= ts.p.page;}

if(pN.sort !== null) {prm[pN.sort]= ts.p.sortname;}

if(pN.order !== null) {prm[pN.order]= ts.p.sortorder;}

...

$.extend(ts.p.postData,prm);

where

prmNames: {page:page,rows:rows, sort: sidx,order: sord, search:_search,

           nd:nd, id:id,oper:oper,editoper:edit,addoper:add,

           deloper:del, subgridid:id, npage: null, totalrows:totalrows}

So to set _search parameter of URL one should set search parameter of jqGrid.

Look at the following demo. You can easy to verify using Fiddler of Firebug that the jqGrid from the page send HTTP GET with the following url:

http://www.ok-soft-gmbh.com/jqGrid/MultisearchFilterAtStart1.json?filters=%7B%22groupOp%22%3A%22AND%22%2C%22rules%22%3A%5B%7B%22field%22%3A%22invdate%22%2C%22op%22%3A%22gt%22%2C%22data%22%3A%222007-09-06%22%7D%2C%7B%22field%22%3A%22invdate%22%2C%22op%22%3A%22lt%22%2C%22data%22%3A%222007-10-04%22%7D%2C%7B%22field%22%3A%22name%22%2C%22op%22%3A%22bw%22%2C%22data%22%3A%22test%22%7D%5D%7D&_search=true&nd=1297508504770&rows=10&page=1&sidx=id&sord=asc

So it do exactly what you need. The code of the demo contain the following code fragment:

$(#list).jqGrid({

    url: 'MultisearchFilterAtStart1.json',

    datatype: json,

    postData: {

        filters:'{groupOp:AND,rules:['+

                '{field:invdate,op:gt,data:2007-09-06}'+

                ',{field:invdate,op:lt,data:2007-10-04}'+

                ',{field:name,op:bw,data:test}]}'

    },

    search:true,

    // ...

});